# lecture11 - Landau free energy density QuickTime and a...

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Landau free energy density QuickTimeª and a decompressor are needed to see this picture. QuickTi decom are neede For large N we expect thermodynamic limit t=(T-T c )/T c (t=0 corresponds to the critical temperature Can think of this as averaging over many spins, ignoring spatial correlations/fluctuations …. like mean field theory QuickTimeª and decompressor are needed to see thi

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Minima of the Landau free energy density QuickTimeª and a decompressor are needed to see this picture. For H=0, t>0, we find η= 0 For H=0, t<0, we find η= 0, t=(T-T c )/T c (t=0 corresponds to the critical temperature) QuickTime decompre are needed to QuickTimeª decompre are needed to
Minimization using Metropolis Monte-Carlo…. Take H=0 and k B T c =1 (L in units of k B T c ) Determine using Metropolis algorithm as a function of T What is the effect of changing N? Notice that T=T c (t+1) a=1 and b=1 in definition of L QuickTi decom are neede QuickTimeª and decompressor are needed to see th Qu de are

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Coding it up… declarations IMPLICIT NONE INTEGER, PARAMETER :: Prec14=SELECTED_REAL_KIND(14) INTEGER , PARAMETER :: mcmax=100000,N=1000,mcmin=mcmax/2 INTEGER :: mc,nt,ntot REAL(KIND=Prec14) :: l1,l2,eta,etalast,prob,rnd,bb,aa,t REAL(KIND=Prec14) :: etaaverage,etaanalytic REAL(KIND=Prec14), PARAMETER :: a=1,b=1,tsteps=100 REAL(KIND=Prec14), PARAMETER :: tmax=1.0d0,tmin=-1.0d0 REAL(KIND=Prec14), PARAMETER :: dtemp=(tmax-tmin)/tsteps REAL(KIND=Prec14), PARAMETER :: step=0.01d0 ! Parameters to go from Landau density to Landau free energy aa=a*N bb=b*N
Outermost “do” loop on reduced temperature t. etaaverage and ntot are for

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lecture11 - Landau free energy density QuickTime and a...

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