Phase diagram for three-dimensional correlated site-bond percolation

Abstract

The Coniglio-Stanley-Klein model is a random bond percolation process between the occupied sites of a lattice gas in thermal equilibrium. Our Monte Carlo simulation for 403 and 603 simple cubic lattices determines at which bond thresholdp Bc , as a function of temperatureT and concentrationx of occupied sites, an infinite network of active bonds connects occupied sites. The curvesp Bc (x, T) depend only slightly onT whereas they cross over if plotted as a function of the field conjugate tox. Except close toT c we find 1/p Bc to be approximated well by a linear function ofx, in the whole interval between the thresholdx c (T) of interacting site percolation atp Bc =1 and the random bond percolation limitx=1 atp Bc =0.248±0.001. Thisx c (T) varied between 0.22 forT=0.96 (coexistence curve) and 0.3117±0.0003 forT=∞ (random site percolation). At the critical point (T=T andx=1/2) we confirmed quite accurately the predictionp Bc =1-exp(−2J/k B T c ) of Coniglio and Klein. As a byproduct we found 0.89±0.01 for the critical exponent of the correlation length in random percolation.