2D Ising Model with Lattice structure

Hayden Stricklin

2019 4 17

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4 次查看（30 天）

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I'm trying to model the Ising model and plot magnetization and energy vs temperature, but it's not quite right. I'm sure it's something tiny like a misplaced comma or something in the wrong for loop, I just need a fresh set of eyes to see it.

clc
clear all
close all
size = 10;
%defining size for the matrix
Tnum = 5;
%temperatures to test
itnum = 10;
%time steps
for t = 1:Tnum
    %temperature steps
    A = ones(size);
    %inital matrix
    TT(t) = (t/Tnum)*5;
    %temperature steps over temp
    %TTT(t) = TT;
    Mag(1, t) = sum(sum(A));
    %magnetization
    E(1,t)=-200;
    %energy
    for i = itnum %time steps
        
        for j = 1:size %part of matrix
            for k = 1:size %part of matrix
               CS = circshift(A, [0 1]) + circshift(A, [0 -1]) + circshift(A, [1 0]) + circshift(A, [-1 0]);
               %circle shifting the matrix
               delE = 2*A(j,k)*CS(j,k);
               %change in total energy
               if delE<=0
                   A(j,k) = -A(j,k);
                   %flipped!
                   continue
               end
                  jjj = -delE/TT(t);
                  chk = exp(jjj);
             
               nn = rand;
               if nn<chk
                   A(j,k) = -1*A(j,k);
                   %no flip, keep
               end
            end
        end
        A
        Mag(i+1,t) = sum(sum(A));
        %pause(0.1)
        %mag at the next step
        CS = circshift(A, [0 1]) + circshift(A, [0 -1]) + circshift(A, [1 0]) + circshift(A, [-1 0]);
        E(i+1,t)=-0.5*sum(sum(A.*CS));    
        %updating energy total
       
    end
    MM(t) = sum(Mag(:,t))/(itnum+1);
    %sum of magnetizations over time steps
    EE(t) = sum(E(:,t))/(itnum+1);
    %sum of energy over time
end
figure(1)
plot(TT, MM)
%plotting temp vs sums of magnetism
hold on
figure(2)
plot(TT, EE)
%plotting temp vs energy