  Phase transitions inside the pores of an aerogel are investigated by
modelizing the aerogel structure by diffusion-limited cluster-cluster
aggregation on a cubic lattice in a finite box and considering $q$-states Potts
variables on the empty sites interacting via nearest-neighbours. Using a finite
size scaling analysing 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 is 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.
