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Cluster Sizes at Equilibrium

I modified my Ising model simulation code a bit to capture the sizes of the clusters formed after 128 time steps. I found that at $T_c = 2.269$ the distribution of cluster sizes is reminiscent of a power law in that it has a very sharp curve (see Figure 32). When plotted on a log-log plot (Figure 33), the distribution appears to be ``linear'' (which indicates a power law distribution). Figure 34 demonstrates the similarity between the cluster distributions and the function $f(x) = x^{-2}$.

Figure 32: Cluster distributions at $T_c = 2.269$.
\begin{figure}\begin{center} \mbox{\epsfig{figure=cluster.eps}} \end{center} \end{figure}

Figure 33: Cluster distributions at $T_c = 2.269$ on a log-log plot.
\begin{figure}\begin{center} \mbox{\epsfig{figure=clusterloglog.eps}} \end{center} \end{figure}

Figure 34: Cluster distributions (as a fraction of the number of clusters of size 1) at $T_c = 2.269$ and the function $f(x) = x^{-2}$ on a log-log plot.
\begin{figure}\begin{center} \mbox{\epsfig{figure=clusterpowlaw.eps}} \end{center} \end{figure}


2005-05-05