Finite-Size Effects in Monte Carlo Simulations of the Gaussian Disorder Model
|
|
- Hugh Dale Greene
- 6 years ago
- Views:
Transcription
1 Journal of the Korean Physical Society, Vol. 60, No. 11, June 2012, pp Finite-Size Effects in Monte Carlo Simulations of the Gaussian Disorder Model Sunil Kim Division of Quantum Phases and Devices, School of Physics, Konkuk University, Seoul , Korea Joonhyun Yeo Division of Quantum Phases and Devices, School of Physics, Konkuk University, Seoul , Korea and School of Physics, Korea Institute for Advanced Study, Seoul , Korea Chan Im Department of Chemistry and Konkuk University-Fraunhofer ISE Next Generation Solar Cell Research Center (KFnSC), Konkuk University, Seoul , Korea Doseok Kim Department of Physics, Sogang University, Seoul , Korea (Received 9 March 2012, in final form 10 April 2012) We study theoretical issues related to the use of finite size systems in Monte Carlo simulations of the Gaussian disorder model (GDM). The GDM is one of the most widely used models to describe the charge transport in random organic materials. In the GDM, the energy of charge carriers is well known to approach an equilibrium energy in the long-time limit. We find that at low temperatures, the equilibrium energy shows a strong dependence on the system size. Using improved numerical methods, we study system sizes much bigger than those used in earlier works. We show that, below a certain temperature, a system size much larger than those used in conventional studies must be used to correctly describe the temperature dependence of the equilibrium energy. PACS numbers: Ee, Le, Bg Keywords: Charge transport, Random organic solids, Gaussian disorder model, Kinetic Monte Carlo method DOI: /jkps I. INTRODUCTION The charge transport in disordered organic materials has been studied both theoretically and experimentally for many years [1]. Among the theoretical models, the so-called Gaussian disorder model (GDM) is probably the most successful and widely used one (see Ref. 2 for a review). In the GDM, a charge carrier hops in an energetically disordered environment, where the energy of localized states is given by a Gaussian distribution with a fixed width. Although there have been some analytical studies [3 6] on this model, many important results, such as a transition from a dispersive to nondispersive transport behavior, have been obtained through numerical Monte Carlo simulations [7 12]. The Monte Carlo simulation on the GDM is relatively easy to implement and has been widely used to understand various problems arising in the charge transport in disordered materials. jhyeo@konkuk.ac.kr These include the effects on the charge transport of the Coulomb interaction among charge carriers [13, 14] and of the morphology of the sample [15]. In order to apply this powerful method to more complicated and realistic situations, it is important to clear any subtle points in the implementation of the method. In this regard, we reexae here a few fundamental aspects of the Monte Carlo simulation of the GDM that have not been received much attention before. One of the key results of the GDM is the relaxation of the energy of charge carriers to an equilibrium energy ɛ, which is responsible for the dispersive-tonondispersive change in the transport behavior [7,8,12]. In this paper, we show that this equilibrium energy crucially depends on the size of the grid points over which the Gaussian energy is distributed. A simple analysis predicts that as a function of temperature T, the equilibrium energy decreases as σ 2 /(k B T ) as the temperature decreases, where σ is the variance of the Gaussian energy distribution and k B is the Boltzmann constant.
2 Journal of the Korean Physical Society, Vol. 60, No. 11, June 2012 This trend, however, is not expected to continue all the way down to zero temperature because of the so-called frustration or freezing effect [4, 5, 16]. At very low temperatures, a thermal activation to a higher energy state, which is necessary to achieve an equilibrium, becomes extremely difficult for a charge carrier subject to a shortrange hopping. Therefore, below a certain temperature T c, the equilibrium energy is expected to increase with decreasing temperature, deviating from the σ 2 /(k B T ) behavior [4,5,16]. In this paper, we show that at moderately low temperatures above T c, Monte Carlo simulations of the GDM exhibit another type of deviation of ɛ from the simple 1/T behavior. It is caused by the use of a finite number of grid points. We explicitly show how the temperature dependence of ɛ varies as the size of the system changes in this temperature region. We develop an improved numerical method to perform simulations with systems whose sizes are much bigger than those used in conventional studies [2,9,17]. We find that at low temperatures, one needs a bigger system size than the conventional one to correctly represent the temperature dependence of ɛ in Monte Carlo simulations. In the next section, we briefly review the main ingredients of the GDM and its Monte Carlo simulations. We then discuss the energy relaxation of the charge carriers and its finite size dependence in detail. We conclude in the following section with some discussion. II. GAUSSIAN DISORDER MODEL The Gaussian disorder model (GDM) [2] is a model describing the charge transport in a disordered energetic landscape. In this section, we briefly review key features of the GDM and of the Monte Carlo simulation methods for the model. The model consists of a cubic lattice of N lattice points that represent localized electronic states. Each lattice point is assigned an energy that is extracted from the Gaussian distribution ρ(ɛ) with a standard deviation σ, ρ (ɛ) = 1 σ 2π exp ( ɛ2 2σ 2 ). (1) In many previous works [2,9,17], a lattice with N =70 3 with a periodic boundary condition has been used. One of the main points of this paper is to investigate how physical quantities depend on the number N of the energetic grids over which the Gaussian energies are distributed. A charge carrier can hop from site i to j with the hopping rate ν ij given by the Miller-Abrahams hopping rule [18] [ ( ν ij = ν 0 exp ( 2γ R ij ) 1, exp ɛ )] j ɛ i,(2) k B T where γ is the wave function overlap parameter, which controls the electronic exchange interaction between sites, R ij is the distance between sites i and j, ɛ i is the energy of site i, k B is the Boltzmann constant and T is the temperature. The value of the pre-factor ν 0 depends on the electron interaction mechanism and is assumed to be on the order of the phonon frequency s 1. Note that the latter part of Eq. (2) is just the Metropolis algorithm. One can use another algorithm that satisfies the detailed balance condition [19]. Computer simulations on the GDM are based on the so-called kinetic Monte Carlo method [20]. In a kinetic Monte Carlo calculation, one needs to know the normalization factor j i ν ij for the whole configuration space. In usual calculations, however, for computational convenience only a box of finite size M is considered for the calculation of the normalization factor. Conventionally the value of M =7 3 has been frequently used. For the overlap parameter 2γa = 10usedinthe present simulation with the lattice constant a, the hopping rate to sites outside a box of this size can indeed be neglected. The probability of hopping from site i to j is then described by ν ij p ij = M j i ν. (3) ij We randomly select a site j tohopaccordingtothese probabilities. The time taken by this move is evaluated as 1 t ij = M j i ν. (4) ij The simulation is performed by repeating this hopping procedure until the charge carrier reaches the end of the sample. We note that given the overlap parameter 2γa, the system is completely described by the dimensionless inverse temperature βσ, whereβ =1/(k B T ). III. ENERGY RELAXATION In the GDM, the mean energy of the charge carrier ɛ(t) at time t is well known to relax toward the equilibrium energy in the long-time limit, ɛ =lim t ɛ (t). This is responsible for the non-dispersive behavior of the charge transport in this model. In this section, we investigate critically the energy relaxation of the GDM, focusingonthefinite-sizeeffectsinthemontecarlosimulation. The charge carrier starts from some high-energy states and moves downward in energy until it reaches the equilibrium energy. The time at which the energy of the charge carrier reaches ɛ is the relaxation time, which increases very rapidly with decreasing temperature [2]. The equilibrium energy ɛ can easily be calculated as ɛρ (ɛ)exp( βɛ) dɛ ɛ = ρ (ɛ)exp( βɛ) dɛ = βσ2. (5)
3 Finite-Size Effects in Monte Carlo Simulations of the Gaussian Disorder Model Sunil Kim et al In order to achieve an equilibrium state, a charge carrier must be able to be thermally activated to a higher energy state for a subsequent energy relaxation process. At very low temperatures, however, an activated jump to a higher energy state becomes extremely difficult once the charge carrier reaches a sufficiently low-lying state. This frustration effect [16] of the relaxation process results in a freezing of the charge carrier energy ɛ (t) at some value higher than that given in Eq. (5). Thus, the decrease in ɛ with decreasing temperature, as in Eq. (5), does not continue all the way down to zero temperature. Instead, below some temperature T c, ɛ will show an upward curvature even with decreasing temperature [16]. In this paper, we focus on moderately low temperatures with T>T c, where full equilibration of charge carrier energy can be achieved within the simulation times and the expression in Eq. (5) can be applied. We note, however, that this expression is valid only for a system of infinite size. The system studied in a simulation has a finite number of states over which the energies are distributed according to the Gaussian density profile ρ(ɛ). Therefore, there will always be a imum energy ɛ (N) for a given number N of states. The average value of can be estimated from ɛ (N) ɛ (N) ρ(ɛ)dɛ 1 N, (6) or more accurately from averaging over the actual imum energies of the Gaussian energy distributions of size N. Since there is no state available with energy less than ɛ (N) for a system of size N, weexpectthatatverylow temperatures, the equilibrium energy will deviate from the one given by Eq. (5). This is clearly seen in Fig. 1. We can actually evaluate the equilibrium energy for afinitesystembyperforgasimplesamplingintegration of Eq. (5). First, we prepare a set of energy states, {ɛ n }, n =1, 2,...,N, by using a Gaussian random number generator with fixed σ. Then, we evaluate the thermal average as ɛ n = n ɛ np n / n p n,where p n =exp( βɛ n ). By averaging this quantity over a number of different Gaussian distributions, we can obtain ɛ (N), which is the finite-size version of Eq. (5). As can be seen from Fig. 1, the actual simulation results for the equilibrium energy do not follow the infinite-system limit given by Eq. (5), but its finite size version ɛ (N), whichis the solid curve in the main panel of Fig. 1. We can also see that this finite-size equilibrium energy approaches the imum energy ɛ (N) in the zero-temperature limit. In previous Monte Carlo simulations of the GDM, the typical size N of energetic grids over which the Gaussian energies are distributed was N = 70 3 = As we can see from Fig. 1, the simulated equilibrium energy in this case does not follow Eq. (5) at temperatures below βσ 3. We expect that the finite-size version of the equilibrium energy ɛ (N) will approach the infinite-system result given in Eq. (5) as N. Fig. 1. The filled squares are the equilibrium energy ɛ /σ as a function of the inverse temperature, βσ, obtained from the Monte Carlo simulation of the GDM for energetic grids of N =70 3. The solid curve is the finite-size prediction, ɛ (N), for N =70 3 (see text). The dashed line is the result for an infinite system, as given by Eq. (5), and the horizontal dotted line indicates the average imum energy, ɛ (N), for N =70 3 obtained numerically. The curves in the inset show the finite-size equilibrium energies ɛ (N) for various numbers N. From top to bottom, N =10 3,30 3, and Thesymbols are the actual simulation data. The straight line is again the result for the infinite system. Fig. 2. The equilibrium energy of the GDM as a function of the size N of grid points. Boxes, circles and triangles represent three different temperatures, βσ = 3.0, 3.5, and 4.0, respectively. The horizontal lines are infinite-size results. The arrow indicates the size N =70 3 used in previous simulations. This is demonstrated in the inset of Fig. 1. We note that the deviation of the finite-size equilibrium energy ɛ (N) from the infinite-system size limit has also been noticed in Ref. 21. We now present actual Monte Carlo results for the equilibrium energy of the GDM for various values of N. The mean energy ɛ(t) is obtained by averaging the en-
4 Journal of the Korean Physical Society, Vol. 60, No. 11, June 2012 ergy of the charge carrier at time t over many trials for a given energetic grid and over different realizations of the Gaussian energy distribution. This quantity decays with time and approaches a constant value ɛ for t greater than the relaxation time. We find that the equilibrium energy ɛ obtained in this way closely follows the finite-size estimate ɛ (N), as shown in Fig. 1. Therefore, in order to evaluate the equilibrium energy correctly at low temperatures βσ 3, one has to use a number N of grid points larger than the conventional We perform Monte Carlo simulations on the GDM for a grid size bigger than the one used in conventional simulations. The simulations were performed for size of N up to We note that simulating the GDM at such large N is not a trivial task. The fastest way to run the simulation would be to store the hopping rates ν ij for all pairs of sites on the grid. For a box of size 7 3 within which a charge carrier hops at a given time, the required memory size is 7 3 8byte 2.6 Kb. If one consider, for example, 70 3 sites, the required memory is about byte 0.9 Gb. Therefore, on a contemporary high-end PC with about 8 Gb memory, the biggest grid size one can study in this way will only be about On the other hand, if we calculate the hopping rate every time a charge carrier jumps, we find that the computation time is about 10 times longer than in the case where all the hopping rates are stored. In the present work, we use an intermediate method where we store the hopping rates only for the sites two or three steps before the current position of the charge carrier. This costs very little in memory, furthermore, it speeds up the computation time significantly especially in low temperature regions. This is possible because at low temperatures, the charge carrier tends to get trapped in a certain energy configuration so that it spends much time oscillating back and forth between two low energy sites. Figure 2 clearly shows that the finite size effect on the equilibrium energy gradually disappears as the system size is increased. However, the system size N =70 3 conventionally used in the Monte Carlo simulations of the GDM does not give an accurate value of the equilibrium energy at low temperatures below βσ 3. In fact, at low temperatures βσ = 3and3.5, the true equilibrium energy is realized only when the system size is as large as the one used in this paper, i.e., N We can also see that a grid size bigger than 10 9 has to be used to correctly describe the equilibrium energy at low temperatures below βσ = 4. IV. DISCUSSION AND CONCLUSION We have investigated in detail some points, which have not been treated in the literature before, in connection with the Monte Carlo simulation of the GDM. Since we are bound to use a finite number of grid points for the Gaussian energy distribution, the temperature dependence of the equilibrium energy will not be that of an infinite-size system, Eq. (5), as commonly assumed. We have calculated a finite-size version of this formula ɛ (N) numerically and have shown that the actual Monte Carlo simulation results follow this finite-size result. We have found that, in order to get rid of any finite-size effects in the equilibrium energy, one needs to consider the size of grid points larger than those used in conventional simulations at low temperatures. In this paper, this has been possible by storing the hopping rates appropriately as the charge carrier hops. As mentioned earlier, all these discussions only apply to moderately low temperatures above T c. At very low temperatures, the relaxation becomes extremely slow [4, 5], and the charge carrier cannot explore the full phase space available to it. Because of this frustration effect, one might say that the charge carrier effectively sees a smaller number of grids. At temperatures below T c, the quasiequilibrium energy will increase with decreasing temperature even for a strictly infinite system. In actual simulations at temperatures below T c, there will also be finite-size effects resulting from the use of a finite number of grids. In this work, the finite-size version of the equilibrium energy ɛ (N) has been calculated by considering only the energetics of localized states, and the actual kinetics of charge carriers is missing, which will be an important factor in the extremely low temperature region. Future numerical works on this quantity at temperatures below T c should show how the frustration effect manifests itself in an actual simulation using a finite number of energetic grids. ACKNOWLEDGMENTS We thank Prof. H. Bässler for useful discussions. This work was supported by the Korean Government (MEST) grant No and by the Seoul R&BD Program (WR090671). S. Kim and J. Yeo were also supported by the WCU program through the KOSEF funded by the MEST (Grant No. R ). D. Kim acknowledges support by the National Research Foundation (NRF) grant funded by the Korea government (MEST) No REFERENCES [1] See, for example, Charge Transport in Disordered Solids with Applications in Electronics, edited by S. Baranovski (John Wiley & Sons, Ltd., Chichester, 2006). [2] H. Bässler, Phys. Status Solidi B 175, 15 (1993). [3] M. Grünwald, B. Pohlmann, B. Movaghar and D. Wurtz, Philos. Mag. B 49, 341 (1984). [4] B. Movaghar, M. Grünwald, B. Ries and H. Bässler, Phys. Rev. B 33, 5545 (1986). [5] B. Movaghar, B. Ries and M. Grünwald, Phys. Rev. B 34, 5574 (1986).
5 Finite-Size Effects in Monte Carlo Simulations of the Gaussian Disorder Model Sunil Kim et al [6] R. Schmechel, Phys. Rev. B 66, (2002). [7] G. Schönherr, H. Bässler and M. Silver, Philos. Mag. B 44, 47 (1981). [8] G. Schönherr, H. Bässler and M. Silver, Philos. Mag. B 44, 369 (1981). [9] L. Pautmeier, R. Richert and H. Bässler, Philos. Mag. Lett. 59, 325 (1989). [10] B. Hartenstein and H. Bässler, J. Non-Cryst. Solids 190, 112 (1995). [11] L. Pautmeier, R. Ichert and H. Bässler, Philos. Mag. B 63, 587 (1991). [12] S. J. Martin, A. Kambili and A. B. Walker, Phys. Rev. B 67, (2003). [13] J. Zhou, Y. C. Zhou, J. M. Zhao, C. Q. Wu, X. M. Ding and X. Y. Hou, Phys. Rev. B 75, (2007). [14] L. Demeyu, S. Stafström and M. Bekele, Phys. Rev. B 76, (2007). [15] S. Raj Mohan, M. P. Joshi and Manoranjan P. Singh, Org. Electron. 9, 355 (2008). [16] S. T. Hoffmann, H. Bässler, J. Koenen, M. Forster, U. Scherf, E. Scheler, P. Strohriegl and A. Köhler, Phys. Rev. B 81, (2010). [17] P. M. Borsenberger, L. T. Pautmeier and H. Bässler, Phys. Rev. B 46, (1992). [18] A. Miller and E. Abrahams, Phys. Rev. 120, 745 (1960). [19] S. V. Novikov, D. H. Dunlap, V. M. Kenkre, P. E. Parris and A. V. Vannikov, Phys. Rev. Lett. 81, 4472 (1998). [20] A. B. Bortz, M. H. Kalos and J. L. Lebowitz, J. Comput. Phys. 17, 10 (1975). [21] A. Lukyanov and D. Andrienko, Phys. Rev. B 82, (2010).
Carrier heating in disordered organic semiconductors
Carrier heating in disordered organic semiconductors Yevgeni Preezant and Nir Tessler* Microelectronic & Nanoelectronic Centers, Electrical Engineering Department, Technion Israel Institute of Technology,
More informationEnergy position of the transport path in disordered organic semiconductors
J. Phys.: Condens. Matter 6 (014) 55801 (10pp) Journal of Physics: Condensed Matter doi:10.1088/095-8984/6/5/55801 Energy position of the transport path in disordered organic semiconductors J O Oelerich
More informationCharge transport in disordered organic solids: A Monte Carlo simulation study on the effects of film morphology
Charge transport in disordered organic solids: A Monte Carlo simulation study on the effects of film morphology S. Raj Mohan, M. P. Joshi * and Manoranjan P. Singh Laser Physics Applications Division,
More informationMonte Carlo Simulation of Ferroelectric Domain Structure: Electrostatic and Elastic Strain Energy Contributions
Monte Carlo Simulation of Ferroelectric Domain Structure: Electrostatic and Elastic Strain Energy Contributions B.G. Potter, Jr., B.A. Tuttle, and V. Tikare Sandia National Laboratories Albuquerque, NM
More informationTopological defects and its role in the phase transition of a dense defect system
Topological defects and its role in the phase transition of a dense defect system Suman Sinha * and Soumen Kumar Roy Depatrment of Physics, Jadavpur University Kolkata- 70003, India Abstract Monte Carlo
More informationAn EAM potential for the dynamical simulation of Ni-Al alloys
J. At. Mol. Sci. doi: 10.4208/jams.022310.031210a Vol. 1, No. 3, pp. 253-261 August 2010 An EAM potential for the dynamical simulation of Ni-Al alloys Jian-Hua Zhang, Shun-Qing Wu, Yu-Hua Wen, and Zi-Zhong
More informationResistance distribution in the hopping percolation model
Resistance distribution in the hopping percolation model Yakov M. Strelniker, Shlomo Havlin, Richard Berkovits, and Aviad Frydman Minerva Center, Jack and Pearl Resnick Institute of Advanced Technology,
More informationMicroscopic Deterministic Dynamics and Persistence Exponent arxiv:cond-mat/ v1 [cond-mat.stat-mech] 22 Sep 1999
Microscopic Deterministic Dynamics and Persistence Exponent arxiv:cond-mat/9909323v1 [cond-mat.stat-mech] 22 Sep 1999 B. Zheng FB Physik, Universität Halle, 06099 Halle, Germany Abstract Numerically we
More informationPressure Dependent Study of the Solid-Solid Phase Change in 38-Atom Lennard-Jones Cluster
University of Rhode Island DigitalCommons@URI Chemistry Faculty Publications Chemistry 2005 Pressure Dependent Study of the Solid-Solid Phase Change in 38-Atom Lennard-Jones Cluster Dubravko Sabo University
More informationJ ij S i S j B i S i (1)
LECTURE 18 The Ising Model (References: Kerson Huang, Statistical Mechanics, Wiley and Sons (1963) and Colin Thompson, Mathematical Statistical Mechanics, Princeton Univ. Press (1972)). One of the simplest
More informationTHE STUDY OF CHARGE CARRIER TRANSPORT ON THE CALAMITIC LIQUID CRYSTALS 5, 5 -DI-(ALKYL-PYRIDIN-YL) - 2 BITHIOPHENES. Abstract
Presented on Gordon Research Conference on Liquid Crystals, June 14-19, 2009, Colby-Sawyer College, New London, NH, USA THE STUDY OF CHARGE CARRIER TRANSPORT ON THE CALAMITIC LIQUID CRYSTALS 5, 5 -DI-(ALKYL-PYRIDIN-YL)
More informationarxiv:cond-mat/ v4 [cond-mat.dis-nn] 23 May 2001
Phase Diagram of the three-dimensional Gaussian andom Field Ising Model: A Monte Carlo enormalization Group Study arxiv:cond-mat/488v4 [cond-mat.dis-nn] 3 May M. Itakura JS Domestic esearch Fellow, Center
More informationarxiv:chem-ph/ v2 11 May 1995
A Monte Carlo study of temperature-programmed desorption spectra with attractive lateral interactions. A.P.J. Jansen Laboratory of Inorganic Chemistry and Catalysis arxiv:chem-ph/9502009v2 11 May 1995
More informationAdvanced Monte Carlo Methods Problems
Advanced Monte Carlo Methods Problems September-November, 2012 Contents 1 Integration with the Monte Carlo method 2 1.1 Non-uniform random numbers.......................... 2 1.2 Gaussian RNG..................................
More informationKinetic Monte Carlo (KMC) Kinetic Monte Carlo (KMC)
Kinetic Monte Carlo (KMC) Molecular Dynamics (MD): high-frequency motion dictate the time-step (e.g., vibrations). Time step is short: pico-seconds. Direct Monte Carlo (MC): stochastic (non-deterministic)
More informationStatistics and Quantum Computing
Statistics and Quantum Computing Yazhen Wang Department of Statistics University of Wisconsin-Madison http://www.stat.wisc.edu/ yzwang Workshop on Quantum Computing and Its Application George Washington
More informationQuantum annealing for problems with ground-state degeneracy
Proceedings of the International Workshop on Statistical-Mechanical Informatics September 14 17, 2008, Sendai, Japan Quantum annealing for problems with ground-state degeneracy Yoshiki Matsuda 1, Hidetoshi
More informationPhysics 115/242 Monte Carlo simulations in Statistical Physics
Physics 115/242 Monte Carlo simulations in Statistical Physics Peter Young (Dated: May 12, 2007) For additional information on the statistical Physics part of this handout, the first two sections, I strongly
More informationCentrifugal Barrier Effects and Determination of Interaction Radius
Commun. Theor. Phys. 61 (2014) 89 94 Vol. 61, No. 1, January 1, 2014 Centrifugal Barrier Effects and Determination of Interaction Radius WU Ning ( Û) Institute of High Energy Physics, P.O. Box 918-1, Beijing
More informationSupplementary information for Tunneling Spectroscopy of Graphene-Boron Nitride Heterostructures
Supplementary information for Tunneling Spectroscopy of Graphene-Boron Nitride Heterostructures F. Amet, 1 J. R. Williams, 2 A. G. F. Garcia, 2 M. Yankowitz, 2 K.Watanabe, 3 T.Taniguchi, 3 and D. Goldhaber-Gordon
More informationNumerical Analysis of 2-D Ising Model. Ishita Agarwal Masters in Physics (University of Bonn) 17 th March 2011
Numerical Analysis of 2-D Ising Model By Ishita Agarwal Masters in Physics (University of Bonn) 17 th March 2011 Contents Abstract Acknowledgment Introduction Computational techniques Numerical Analysis
More informationarxiv:cond-mat/ v2 [cond-mat.soft] 10 Mar 2006
An energy landscape model for glass-forming liquids in three dimensions arxiv:cond-mat/v [cond-mat.soft] Mar Ulf R. Pedersen, Tina Hecksher, Jeppe C. Dyre, and Thomas B. Schrøder Department of Mathematics
More informationPopulation Annealing: An Effective Monte Carlo Method for Rough Free Energy Landscapes
Population Annealing: An Effective Monte Carlo Method for Rough Free Energy Landscapes Jon Machta SFI WORKING PAPER: 21-7-12 SFI Working Papers contain accounts of scientific work of the author(s) and
More informationA New Method to Determine First-Order Transition Points from Finite-Size Data
A New Method to Determine First-Order Transition Points from Finite-Size Data Christian Borgs and Wolfhard Janke Institut für Theoretische Physik Freie Universität Berlin Arnimallee 14, 1000 Berlin 33,
More informationKinetic Monte Carlo simulation of semiconductor quantum dot growth
Solid State Phenomena Online: 2007-03-15 ISSN: 1662-9779, Vols. 121-123, pp 1073-1076 doi:10.4028/www.scientific.net/ssp.121-123.1073 2007 Trans Tech Publications, Switzerland Kinetic Monte Carlo simulation
More informationRecursive Speed-up in Partition Function Evaluation
Recursive Speed-up in Partition Function Evaluation A. Balaž, A. Belić and A. Bogojević Institute of Physics, P.O.B. 57, Belgrade, Yugoslavia Abstract We present a simple recursive relation that leads
More informationOptical time-domain differentiation based on intensive differential group delay
Optical time-domain differentiation based on intensive differential group delay Li Zheng-Yong( ), Yu Xiang-Zhi( ), and Wu Chong-Qing( ) Key Laboratory of Luminescence and Optical Information of the Ministry
More informationPhase Transitions of an Epidemic Spreading Model in Small-World Networks
Commun. Theor. Phys. 55 (2011) 1127 1131 Vol. 55, No. 6, June 15, 2011 Phase Transitions of an Epidemic Spreading Model in Small-World Networks HUA Da-Yin (Ù ) and GAO Ke (Ô ) Department of Physics, Ningbo
More informationIs the Sherrington-Kirkpatrick Model relevant for real spin glasses?
Is the Sherrington-Kirkpatrick Model relevant for real spin glasses? A. P. Young Department of Physics, University of California, Santa Cruz, California 95064 E-mail: peter@physics.ucsc.edu Abstract. I
More informationPhase Transitions in Spin Glasses
Phase Transitions in Spin Glasses Peter Young Talk available at http://physics.ucsc.edu/ peter/talks/sinica.pdf e-mail:peter@physics.ucsc.edu Supported by the Hierarchical Systems Research Foundation.
More informationExcess 1/f noise in systems with an exponentially wide spectrum of resistances and dual universality of the percolation-like noise exponent
Excess 1/f noise in systems with an exponentially wide spectrum of resistances and dual universality of the percolation-like noise exponent A. A. Snarski a) Ukrainian National Technical University KPI,
More informationMD Thermodynamics. Lecture 12 3/26/18. Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
MD Thermodynamics Lecture 1 3/6/18 1 Molecular dynamics The force depends on positions only (not velocities) Total energy is conserved (micro canonical evolution) Newton s equations of motion (second order
More informationCondensed matter theory Lecture notes and problem sets 2012/2013
Condensed matter theory Lecture notes and problem sets 2012/2013 Dmitri Ivanov Recommended books and lecture notes: [AM] N. W. Ashcroft and N. D. Mermin, Solid State Physics. [Mar] M. P. Marder, Condensed
More informationMetropolis/Variational Monte Carlo. Microscopic Theories of Nuclear Structure, Dynamics and Electroweak Currents June 12-30, 2017, ECT*, Trento, Italy
Metropolis/Variational Monte Carlo Stefano Gandolfi Los Alamos National Laboratory (LANL) Microscopic Theories of Nuclear Structure, Dynamics and Electroweak Currents June 12-30, 2017, ECT*, Trento, Italy
More informationarxiv:cond-mat/ v1 19 Sep 1995
Large-scale Simulation of the Two-dimensional Kinetic Ising Model arxiv:cond-mat/9509115v1 19 Sep 1995 Andreas Linke, Dieter W. Heermann Institut für theoretische Physik Universität Heidelberg Philosophenweg
More informationarxiv:nucl-th/ v2 26 Feb 2002
NEGAIVE SPECIFIC HEA IN OU-OF-EQUILIBRIUM NONEXENSIVE SYSEMS A. Rapisarda and V. Latora Dipartimento di Fisica e Astronomia, Università di Catania and INFN Sezione di Catania, Corso Italia 57, I-95129
More information(PP) rrap3ht/c 61 PCBM (Fig. 2e) MEHPPV/C 61 PCBM (Fig. 2f) Supplementary Table (1) device/figure a HF (mt) J (mt) (CTE) 4 2 >1 0.
Supplementary Table (1) device/figure a HF (mt) J (mt) (CTE) S / T (PP) (PP) rrp3ht/pcbm (Fig. b) rrp3ht/pcbm (Fig. c) PBT7/C 71 PCBM (Fig. d) 4 >1 0.6 4 >1 0.6-0 >1 0.7 rrap3ht/c 61 PCBM (Fig. e) 4
More informationQuantum phase transition and conductivity of parallel quantum dots with a moderate Coulomb interaction
Journal of Physics: Conference Series PAPER OPEN ACCESS Quantum phase transition and conductivity of parallel quantum dots with a moderate Coulomb interaction To cite this article: V S Protsenko and A
More informationFrom The Picture Book of Quantum Mechanics, S. Brandt and H.D. Dahmen, 4th ed., c 2012 by Springer-Verlag New York.
1 Fig. 6.1. Bound states in an infinitely deep square well. The long-dash line indicates the potential energy V (x). It vanishes for d/2 < x < d/2 and is infinite elsewhere. Points x = ±d/2 are indicated
More informationEnergy-Decreasing Dynamics in Mean-Field Spin Models
arxiv:cond-mat/0210545 v1 24 Oct 2002 Energy-Decreasing Dynamics in Mean-Field Spin Models L. Bussolari, P. Contucci, M. Degli Esposti, C. Giardinà Dipartimento di Matematica dell Università di Bologna,
More informationParallel Tempering Algorithm in Monte Carlo Simulation
Parallel Tempering Algorithm in Monte Carlo Simulation Tony Cheung (CUHK) Kevin Zhao (CUHK) Mentors: Ying Wai Li (ORNL) Markus Eisenbach (ORNL) Kwai Wong (UTK/ORNL) Metropolis Algorithm on Ising Model
More informationarxiv: v1 [cond-mat.stat-mech] 6 Mar 2008
CD2dBS-v2 Convergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models Burhan Bakar and Ugur Tirnakli Department of Physics, Faculty of Science, Ege University, 35100 Izmir, Turkey
More informationLab 70 in TFFM08. Curie & Ising
IFM The Department of Physics, Chemistry and Biology Lab 70 in TFFM08 Curie & Ising NAME PERS. -NUMBER DATE APPROVED Rev Aug 09 Agne 1 Introduction Magnetic materials are all around us, and understanding
More informationMultiple time step Monte Carlo
JOURNAL OF CHEMICAL PHYSICS VOLUME 117, NUMBER 18 8 NOVEMBER 2002 Multiple time step Monte Carlo Balázs Hetényi a) Department of Chemistry, Princeton University, Princeton, NJ 08544 and Department of Chemistry
More informationKinetic Monte Carlo (KMC)
Kinetic Monte Carlo (KMC) Molecular Dynamics (MD): high-frequency motion dictate the time-step (e.g., vibrations). Time step is short: pico-seconds. Direct Monte Carlo (MC): stochastic (non-deterministic)
More informationExploring the energy landscape
Exploring the energy landscape ChE210D Today's lecture: what are general features of the potential energy surface and how can we locate and characterize minima on it Derivatives of the potential energy
More informationGiant Enhancement of Quantum Decoherence by Frustrated Environments
ISSN 0021-3640, JETP Letters, 2006, Vol. 84, No. 2, pp. 99 103. Pleiades Publishing, Inc., 2006.. Giant Enhancement of Quantum Decoherence by Frustrated Environments S. Yuan a, M. I. Katsnelson b, and
More informationGas-liquid phase separation in oppositely charged colloids: stability and interfacial tension
7 Gas-liquid phase separation in oppositely charged colloids: stability and interfacial tension We study the phase behaviour and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive
More informationFrom Order to Disorder
ORGANIC ELECTRONICS Principles, devices and applications Charge Transport D. Natali Milano, 15-18 Novembre 011 From Order to Disorder From delocalized to localized states 1 The Two-Site approximation a,v
More informationMonte Carlo simulation calculation of the critical coupling constant for two-dimensional continuum 4 theory
Monte Carlo simulation calculation of the critical coupling constant for two-dimensional continuum 4 theory Will Loinaz * Institute for Particle Physics and Astrophysics, Physics Department, Virginia Tech,
More informationHeinonen, J.; Koponen, I.; Merikoski, J.; Ala-Nissilä, Tapio Island diffusion on metal fcc(100) surfaces
Powered by TCPDF (www.tcpdf.org) This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Heinonen, J.; Koponen, I.; Merikoski,
More informationCharge transport in Disordered Organic Semiconductors. Eduard Meijer Dago de Leeuw Erik van Veenendaal Teun Klapwijk
Charge transport in Disordered Organic Semiconductors Eduard Meijer Dago de Leeuw Erik van Veenendaal eun Klapwijk Outline Introduction: Ordered vs. Disordered semiconductors he field-effect transistor
More information6 Description of Charge Transport in Disordered Organic Materials
6 Description of Charge Transport in Disordered Organic Materials S.D. Baranovski and O. Rubel Faculty of Physics and Material Sciences Center, Philipps Universität Marburg, Germany 6.1 Introduction 6.
More informationThe A T emission of KCl:Tl interpreted as a double A T +A X emission
The A T emission of KCl:Tl interpreted as a double A T +A X emission D. Mugnai, G. P. Pazzi, P. Fabeni, and A. Ranfagni Nello Carrara Institute of Applied Physics, CNR Florence Research Area, Via Madonna
More informationFinite Element Analysis of Transient Ballistic-Diffusive Heat Transfer in Two-Dimensional Structures
014 COMSOL Conference, Boston, MA October 7-9, 014 Finite Element Analysis of Transient Ballistic-Diffusive Heat Transfer in Two-Dimensional Structures Sina Hamian 1, Toru Yamada, Mohammad Faghri 3, and
More informationPhase Transitions in Relaxor Ferroelectrics
Phase Transitions in Relaxor Ferroelectrics Matthew Delgado December 13, 2005 Abstract This paper covers the properties of relaxor ferroelectrics and considers the transition from the paraelectric state
More informationEnd-to-end length of a stiff polymer
End-to-end length of a stiff polymer Jellie de Vries April 21st, 2005 Bachelor Thesis Supervisor: dr. G.T. Barkema Faculteit Btawetenschappen/Departement Natuur- en Sterrenkunde Institute for Theoretical
More informationA variational approach to Ising spin glasses in finite dimensions
. Phys. A: Math. Gen. 31 1998) 4127 4140. Printed in the UK PII: S0305-447098)89176-2 A variational approach to Ising spin glasses in finite dimensions R Baviera, M Pasquini and M Serva Dipartimento di
More informationSimulation of the two-dimensional square-lattice Lenz-Ising model in Python
Senior Thesis Simulation of the two-dimensional square-lattice Lenz-Ising model in Python Author: Richard Munroe Advisor: Dr. Edward Brash 2012-10-17 Abstract A program to simulate the the two-dimensional
More informationTwo-dimensional electron-hole capture in a disordered hopping system
PHYSICAL REVIEW B 68, 45301 003 Two-dimensional electron-hole capture in a disordered hopping system N. C. Greenham Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom P. A. Bobbert
More informationInvaded cluster dynamics for frustrated models
PHYSICAL REVIEW E VOLUME 57, NUMBER 1 JANUARY 1998 Invaded cluster dynamics for frustrated models Giancarlo Franzese, 1, * Vittorio Cataudella, 1, * and Antonio Coniglio 1,2, * 1 INFM, Unità di Napoli,
More informationMarkov Chain Monte Carlo The Metropolis-Hastings Algorithm
Markov Chain Monte Carlo The Metropolis-Hastings Algorithm Anthony Trubiano April 11th, 2018 1 Introduction Markov Chain Monte Carlo (MCMC) methods are a class of algorithms for sampling from a probability
More informationQuantum Annealing in spin glasses and quantum computing Anders W Sandvik, Boston University
PY502, Computational Physics, December 12, 2017 Quantum Annealing in spin glasses and quantum computing Anders W Sandvik, Boston University Advancing Research in Basic Science and Mathematics Example:
More informationPHYSICS 219 Homework 2 Due in class, Wednesday May 3. Makeup lectures on Friday May 12 and 19, usual time. Location will be ISB 231 or 235.
PHYSICS 219 Homework 2 Due in class, Wednesday May 3 Note: Makeup lectures on Friday May 12 and 19, usual time. Location will be ISB 231 or 235. No lecture: May 8 (I m away at a meeting) and May 29 (holiday).
More informationFrom time series to superstatistics
From time series to superstatistics Christian Beck School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E 4NS, United Kingdom Ezechiel G. D. Cohen The Rockefeller University,
More informationTriplet state diffusion in organometallic and organic semiconductors
Triplet state diffusion in organometallic and organic semiconductors Prof. Anna Köhler Experimental Physik II University of Bayreuth Germany From materials properties To device applications Organic semiconductors
More informationIn-class exercises. Day 1
Physics 4488/6562: Statistical Mechanics http://www.physics.cornell.edu/sethna/teaching/562/ Material for Week 8 Exercises due Mon March 19 Last correction at March 5, 2018, 8:48 am c 2017, James Sethna,
More informationRenormalization Group: non perturbative aspects and applications in statistical and solid state physics.
Renormalization Group: non perturbative aspects and applications in statistical and solid state physics. Bertrand Delamotte Saclay, march 3, 2009 Introduction Field theory: - infinitely many degrees of
More informationSurfaces, Interfaces, and Layered Devices
Surfaces, Interfaces, and Layered Devices Building blocks for nanodevices! W. Pauli: God made solids, but surfaces were the work of Devil. Surfaces and Interfaces 1 Interface between a crystal and vacuum
More informationThe Phase Transition of the 2D-Ising Model
The Phase Transition of the 2D-Ising Model Lilian Witthauer and Manuel Dieterle Summer Term 2007 Contents 1 2D-Ising Model 2 1.1 Calculation of the Physical Quantities............... 2 2 Location of the
More informationSurface effects in frustrated magnetic materials: phase transition and spin resistivity
Surface effects in frustrated magnetic materials: phase transition and spin resistivity H T Diep (lptm, ucp) in collaboration with Yann Magnin, V. T. Ngo, K. Akabli Plan: I. Introduction II. Surface spin-waves,
More informationThermodynamics of nuclei in thermal contact
Thermodynamics of nuclei in thermal contact Karl-Heinz Schmidt, Beatriz Jurado CENBG, CNRS/IN2P3, Chemin du Solarium B.P. 120, 33175 Gradignan, France Abstract: The behaviour of a di-nuclear system in
More informationarxiv:cond-mat/ v1 [cond-mat.other] 5 Jun 2004
arxiv:cond-mat/0406141v1 [cond-mat.other] 5 Jun 2004 Moving Beyond a Simple Model of Luminescence Rings in Quantum Well Structures D. Snoke 1, S. Denev 1, Y. Liu 1, S. Simon 2, R. Rapaport 2, G. Chen 2,
More informationDensity and temperature of fermions and bosons from quantum fluctuations
Density and temperature of fermions and bosons from quantum fluctuations Hua Zheng and Aldo Bonasera 1 1 Laboratori Nazionali del Sud, INFN, via Santa Sofia, 6, 951 Catania, Italy In recent years, the
More informationMonte Carlo Simulation of Ferroelectric Domain Structure: Electrostatic and Elastic Strain Energy Contributions
f.... Monte Carlo Simulation of Ferroelectric Domain Structure: Electrostatic and Elastic Strain Energy Contributions o (n -+ B.G. Potter, Jr., B.A. Tuttle, and V. Tikare Sandia National Laboratories Albuquerque,
More informationTwo simple lattice models of the equilibrium shape and the surface morphology of supported 3D crystallites
Bull. Nov. Comp. Center, Comp. Science, 27 (2008), 63 69 c 2008 NCC Publisher Two simple lattice models of the equilibrium shape and the surface morphology of supported 3D crystallites Michael P. Krasilnikov
More informationQuantum Monte Carlo simulation of spin-polarized tritium
Higher-order actions and their applications in many-body, few-body, classical problems Quantum Monte Carlo simulation of spin-polarized tritium I. Bešlić, L. Vranješ Markić, University of Split, Croatia
More informationV He C ( r r i ), (1)
PHYSICAL REVIEW B 85, 224501 (2012) 4 He adsorption on a single graphene sheet: Path-integral Monte Carlo study Yongkyung Kwon 1 and David M. Ceperley 2 1 Division of Quantum Phases and Devices, School
More informationTHE DETAILED BALANCE ENERGY-SCALED DISPLACEMENT MONTE CARLO ALGORITHM
Molecular Simulation, 1987, Vol. 1, pp. 87-93 c Gordon and Breach Science Publishers S.A. THE DETAILED BALANCE ENERGY-SCALED DISPLACEMENT MONTE CARLO ALGORITHM M. MEZEI Department of Chemistry, Hunter
More informationOptimization in random field Ising models by quantum annealing
Optimization in random field Ising models by quantum annealing Matti Sarjala, 1 Viljo Petäjä, 1 and Mikko Alava 1 1 Helsinki University of Techn., Lab. of Physics, P.O.Box 1100, 02015 HUT, Finland We investigate
More information0.8 b
k z (Å -1 ).8 a.6 - - -.6 1 3 q CDW.5 1. FS weight -.8 -.8 -.8.8 b.6 1 3 - - -.6 -.8.1.3-1 -1 DOS (states ev u.c. ) -1 Band Energy (evu.c. ) 4 3 1 55 54 53 5 c d w/ CDW w/o CDW -.6 - - E Supplementary
More informationDynamics of Solitary Waves Induced by Shock Impulses in a Linear Atomic Chain*
Dynamics of Solitary Waves Induced by Shock Impulses in a Linear Atomic Chain* PHUOC X. TRAN, DONALD W. BRENNER, and C. T. WHITE Naval Research Laboratory, Washington, DC 20375-5000 Abstract The propagation
More informationarxiv: v1 [cond-mat.dis-nn] 25 Apr 2018
arxiv:1804.09453v1 [cond-mat.dis-nn] 25 Apr 2018 Critical properties of the antiferromagnetic Ising model on rewired square lattices Tasrief Surungan 1, Bansawang BJ 1 and Muhammad Yusuf 2 1 Department
More informationSegregation in a noninteracting binary mixture
Segregation in a noninteracting binary mixture Filip Krzyżewski and Magdalena A. Załuska-Kotur,2 Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland 2 Faculty of
More informationUniversity of Groningen
University of Groningen Universal arrhenius temperature activated charge transport in diodes from disordered organic semiconductors Craciun,. I.; Wildeman, J.; Blom, P. W. M. Published in: Physical Review
More informationarxiv: v1 [cond-mat.dis-nn] 13 Jul 2015
Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network arxiv:1507.03305v1 [cond-mat.dis-nn] 13 Jul 2015 Tasrief Surungan 1,3, Freddy P. Zen 2,3, and Anthony G. Williams 4 1
More informationMetropolis Monte Carlo simulation of the Ising Model
Metropolis Monte Carlo simulation of the Ising Model Krishna Shrinivas (CH10B026) Swaroop Ramaswamy (CH10B068) May 10, 2013 Modelling and Simulation of Particulate Processes (CH5012) Introduction The Ising
More informationGibbs ensemble simulation of phase equilibrium in the hard core two-yukawa fluid model for the Lennard-Jones fluid
MOLECULAR PHYSICS, 1989, VOL. 68, No. 3, 629-635 Gibbs ensemble simulation of phase equilibrium in the hard core two-yukawa fluid model for the Lennard-Jones fluid by E. N. RUDISILL and P. T. CUMMINGS
More informationA =, where d n w = dw
Chapter 9 Monte Carlo Simulations So far we have either dealt with exactly soluble systems like the (time-dependent) oscillator or with various expansions like the semiclassical, perturbative and high-temperature
More informationarxiv: v1 [cond-mat.stat-mech] 6 Mar 2015
Incommensurate Single-Angle Spiral Orderings of Classical Heisenberg Spins on Zigzag Ladder Lattices Yu. I. Dublenych Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1
More informationUniversality class of triad dynamics on a triangular lattice
Universality class of triad dynamics on a triangular lattice Filippo Radicchi,* Daniele Vilone, and Hildegard Meyer-Ortmanns School of Engineering and Science, International University Bremen, P. O. Box
More informationMonte Carlo Study of Planar Rotator Model with Weak Dzyaloshinsky Moriya Interaction
Commun. Theor. Phys. (Beijing, China) 46 (2006) pp. 663 667 c International Academic Publishers Vol. 46, No. 4, October 15, 2006 Monte Carlo Study of Planar Rotator Model with Weak Dzyaloshinsky Moriya
More informationSuperfluidity in Hydrogen-Deuterium Mixed Clusters
Journal of Low Temperature Physics - QFS2009 manuscript No. (will be inserted by the editor) Superfluidity in Hydrogen-Deuterium Mixed Clusters Soomin Shim Yongkyung Kwon Received: date / Accepted: date
More informationSUPPLEMENTARY INFORMATION
Supporting online material SUPPLEMENTARY INFORMATION doi: 0.038/nPHYS8 A: Derivation of the measured initial degree of circular polarization. Under steady state conditions, prior to the emission of the
More informationReconstruction and intermixing in thin Ge layers on Si 001
Reconstruction and intermixing in thin Ge layers on Si 001 L. Nurminen, 1 F. Tavazza, 2 D. P. Landau, 1,2 A. Kuronen, 1 and K. Kaski 1 1 Laboratory of Computational Engineering, Helsinki University of
More informationSpontaneous Magnetization in Diluted Magnetic Semiconductor Quantum Wells
Journal of the Korean Physical Society, Vol. 50, No. 3, March 2007, pp. 834 838 Spontaneous Magnetization in Diluted Magnetic Semiconductor Quantum Wells S. T. Jang and K. H. Yoo Department of Physics
More informationPhysics 127c: Statistical Mechanics. Application of Path Integrals to Superfluidity in He 4
Physics 17c: Statistical Mechanics Application of Path Integrals to Superfluidity in He 4 The path integral method, and its recent implementation using quantum Monte Carlo methods, provides both an intuitive
More informationOpen Access. Suman Chakraborty* Q T + S gen = 1 S 1 S 2. Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur , India
he Open hermodynamics Journal, 8,, 6-65 6 Open Access On the Role of External and Internal Irreversibilities towards Classical Entropy Generation Predictions in Equilibrium hermodynamics and their Relationship
More informationarxiv: v1 [physics.comp-ph] 14 Nov 2014
Variation of the critical percolation threshold in the Achlioptas processes Paraskevas Giazitzidis, 1 Isak Avramov, 2 and Panos Argyrakis 1 1 Department of Physics, University of Thessaloniki, 54124 Thessaloniki,
More informationIntroduction to Relaxation Theory James Keeler
EUROMAR Zürich, 24 Introduction to Relaxation Theory James Keeler University of Cambridge Department of Chemistry What is relaxation? Why might it be interesting? relaxation is the process which drives
More information