Monte Carlo studies of two-dimensional percolation

Abstract

A one-spin flip Ising model is used to provide data on cluster statistics for random and Ising percolation. The concentration p is controlled by the magnetic field. At sufficiently high temperatures the system corresponds to random percolation, and the theoretical formula s/n=(1-p)/p is verified for large clusters at critical concentration pc (s=number of boundary sites). It is also found that the relation is accurately satisfied for all percolating clusters when p>pc but not for Ising percolation at temperature 2Tc. For random percolation with p>pc the finite n-clusters are found to follow an asymptotic decay of the form exp (-b(p)n12/) in accord with theory.