Landau Theory. Many phase transitions exhibit similar behaviors: critical temperature, order parameter

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Lndu ery Intrdutin Mny pse trnsitins exibit simir bevirs: riti temperture, rder prmeter n ne find rter simpe unifying tery tt gives gener penmengi verview f pse trnsitins? Sever ppres : Meur fied (Weiss ~95: sve te Srödinger equtin fr ne prtie system but wit n effetive intertin ptenti : Ĥ p V m Mirspi mde (Ising 9: sve te Srödinger equtin fr pseud spins n ttie wit effetive intertin Hmitnin restrited t first neigbrs Ĥ Ĥ J óió j i, j eff

Lndu ery Intrdutin Lndu ery : Express term dynmi ptenti s funtin f te rder prmeter (, its njugted extern fied ( nd temperture. Keep se t stbe stte minimum f energy pwer series expnsin, eg. ike: ( Find nd disuss minim f versus temperture nd extern fied. Lk t termdynmis prperties (tent et, speifi et, suseptibiity, et. in rder t ssify pse trnsitins

Lndu ery rken symmetry simpe D meni iustrtin : d E pt k ( k ( d x x et g wit d > : equiibrium psitin (minimum energy x =

Lndu ery rken symmetry simpe D meni iustrtin : d E pt k ( k ( d x x et g wit d < : equiibrium psitin (minimum energy x = x Order prmeter @ riti vue d = spntneus symmetry breking Ony irreversibe mirspi events wi mke te system sette t +x r x wen te system swy exnges energy wit extern wrd x d d

rken symmetry Lndu ery simpe D meni iustrtin : d x pt d E x ( k ( k yr expnsin f ptenti (esti energy d d d d x x d (d ( x d d (d (d ( E pt x k x k k k

rken symmetry Lndu ery simpe D meni iustrtin : d x pt d E x ( k ( k yr expnsin f ptenti (esti energy ( E E pt x O x x d (d d (d k nge sign t d=d!!! Des nt nge sign

Lndu ery Send Order Pse rnsitins = >> ( = ( << = stbe bve, unstbe bew

Lndu ery Send Order Pse rnsitins Sttinry sutin : & ( ( ( -

Lndu ery Send Order Pse rnsitins Free energy : ( - ( S( - S ( Entrpy : S N Ltent Het: S =

Lndu ery Send Order Pse rnsitins Speifi et : p S p -

Send Order Pse rnsitins Lndu ery Suseptibiity : ( ( ( eq ( ( - ( 3 urie w -

Lndu ery Send Order Pse rnsitins fied ysteresis : ( 3

Lndu ery Send Order Pse rnsitins SUMMRY One riti temperture N disntinuity f,, S (n tent et t Jump f p t Divergene f nd t Fied ysteresis

Lndu ery First Order Pse rnsitins: ( ( ( t frm nd rder > : = stbe >> = >> > > : = stbe metstbe > > : = metstbe stbe > : stbe

Lndu ery First Order Pse rnsitins: ( ( > : = stbe equ. > > : = stbe metstbe > > : = metstbe stbe > : stbe erm ysteresis

Lndu ery First Order Pse rnsitins: ( ( Stedy stte : +? imit wen ( (

( First Order Pse rnsitins: Lndu ery ( 3 Stedy stte : = 3 3 (

( First Order Pse rnsitins: Lndu ery ( Entrpy : = S S nd depend n! S -S = 8 3 S et Ltent

( First Order Pse rnsitins: Lndu ery ( Speifi et : S S p = p p

( First Order Pse rnsitins: Lndu ery ( Suseptibiity : 5 3 : = stbe unti dwn t 5 3 : - -

Lndu ery First Order Pse rnsitins SUMMRY Existene f metstbe pses emperture dmin ( fr existene f ig nd w temperture pses t ( < < bt ig nd w teperture pses re stbe emperture ysteresis Disntinuity f,, S (tent et, p, t

ririti pint Lndu ery In te frmism f first rder pse trnsitins, it n ppen tt prmeter nges sign under te effet f n extern fied. en tere is pint, wi is ed tririti pint, were =. e Lndu expnsin ten tkes te fwing frm: ( Equiibrium nditins : - 5 - pur pur pur pur

Lndu ery ririti pint Ptenti : >: = >: 3 3 3 3

Lndu ery Entrpy : S S nd depend n! S-S S ririti pint >: = S >: S 3 S S

Lndu ery Speifi et : S p ririti pint >: = p >: p p 3 - p p

Lndu ery ririti pint Suseptibiity : 5 - >: = - >: -

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