Résumé
Phase transitions inside the aerogel pores were investigated by modeling the aerogel structure by diffusion-limited cluster-cluster aggregation on a cubic lattice in a finite box and considering
q-state Potts variables on the empty sites interacting via nearest neighbours. Using a finite size scaling analysis of Monte Carlo numerical results, it is concluded that for
q = 4 the transition changes from first-order to second-order as the aerogel concentration (density) increases. Comparison was made with the case
q = 3 (where the first-order transition is weaker in three dimensions) and with the case
q = 4 but for randomly (non-correlated) occupied sites. Possible applications to experiments are discussed.