Phase diagram for three-dimensional correlated site-bond percolation

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.