epsilon expansion for correlated percolation: applications to gels

The momentum space renormalisation group is applied to a Hamiltonian which describes site-bond correlated percolation, which in turn models the sol-gel transition when solvent effects are present. Mean field theory is used to determine the qualitative features of the phase diagram which includes sol and gel phases in either one- or two-phase regions. Recursion relations in d=6- epsilon dimensions are derived and are shown to have a fixed point corresponding to simultaneous gelation and phase separation. At this fixed point, the critical exponents describing phase separation are the same as for the Ising model nu 0 = 1 / 2 , eta =0 for d>4 whereas those describing gelation differ from those for the usual percolation problem: nu 1 =2/(d-2), eta 1 =0 for 4<d<6.