Fig.8.1: On a square lattice of size 100 x 100, spin configuration at temperature , corresponds to is shown. t is the MC time step per spin.

Fig.8.2: On a square lattice of size 100 x 100, spin configuration at , corresponds to ( ). t is the MC time step per spin.

Spin configurations of a 2d zero field spin- 1/2 Ising model on the square lattice are obtained using single spin flip Metropolis algorithm at a temperature T below in Fig.8.1 and above in Fig.82. The spin configurations shown in the figures above are obtained on a 100 x 100 square lattice. Note that, in absence of the field, the model has up-down symmetry so the overturning all the spins produce a degenerate state. At high temperature all the clusters of like spins are small, near the transition there is a broad distribution of clusters, and at low temperatures there is a single large cluster of ordered spins and a number of small clusters of oppositely directed spins.