Monte-Carlo simulation of Ising droplets in correlated site-bond percolation

Abstract

The definition of droplets in the Ising model by Coniglio and Klein is investigated numerically on square and simple cubic lattices. Our data are consistent with their prediction that the droplets diverge at T c : for 16 × 16 × 17 lattices, the divergence occurs at T/ Tc = 1.02. Above Tc in three dimensions and zero magnetic field, as a function of the concentration of active bonds, we find about the same critical exponent v = 0.9 as for random percolation; but the percolation threshold is twice as large