Numerical Study of Phase Transitions in the Pores of an Aerogel

An aerogel of volume fraction c is modeled on a 3D lattice using diffusion-limited cluster-cluster aggregation in cubic boxes of sizes up to 20 ×{} 20 ×{} 20. A set of q-state Potts variables are disposed on the nonoccupied sites and their order-disorder phase transition is studied by means of a Monte Carlo technique for $q=3$ and $q=4$. It is found that the transition changes from first to second order above a nonzero threshold value of c. A comparison is made with the case of randomly occupied sites. The possible application to recent experimental results is discussed.