Evidence for Fisher's Droplet Model in Simulated Two-Dimensional Cluster Distributions

Abstract

The distribution function $n_l$ of clusters with $l$ reversed spins has been calculated for two square $N\times N$ Ising lattices ($N=55\mathrm{} \mathrm{and} 110$) at various temperatures $T<\mathrm{}{T}_c$ using periodic boundary conditions. These calculations strongly support the cluster model proposed by Fisher and yield the exponent $\tau =2.1\mathrm{}\pm 0.1$. However, for small $l$, $T$ not close to $T_c$, and $H\ne 0$, we find considerable deviations.