Equilibrium phase transitions in a porous medium

Static critical phenomena of a three-dimensional Ising model confined in a porous medium made by spinodal decomposition have been studied using large-scale Monte Carlo simulations. We thus examine the influence of the geometry of Vycor-like materials on phase transitions. No surface interactions (preference of the Vycor-like material for one phase above the other) are taken into account. We find that the critical temperature depends on the average pore size D as Tc(D)=Tc({∞})-c/D. The critical exponents are independent of pore size: we find {ν}=0.8±{}0.1, {γ}=1.4±{}0.1, {β}=0.65±{}0.13. No divergence is observed for the specific heat, indicating {α}{≤}0. All data for all pore sizes can be collapsed well with the scaling function for the magnetic susceptibility {χ}L^-γ/ν={χ} ̃ \~{}{}(tL^1/ν), where t=T/Tc(D)-1. These critical phenomena are consistent with those computed for the randomly site-diluted Ising model. Experimental realizations of our numerical experiments are discussed. {} 1996 The American Physical Society.