5.3 Measurements

Simulations are performed on a 2d square lattice of size 100 x 100. Measurements are done after time steps and averaged over configurations.

The magnetization m per spin in a state n is given by

Since only one spin k flips at a time in the Metropolis algorithm, so the change in magnetization is given by

One can then calculate the magnetization at the beginning of the simulation and then use the following equation

for every spin flip. As soon as the magnetization is obtained, one could calculate the per spin susceptibility as

m and χ are obtained as a function temperature T and are plotted in Figure.4.

Fig.8.5: Plot of magnetization M and susceptibility χ against temperature T (in units of ).

Fig.8.6: Plot of internal energy E and specific heat against temperature T (in units of ).