Random networks of crosslinked manifolds

We generalize the statistical mechanical theory of vulcanization to the case of D-dimensional polymerized manifolds. Starting from a continuum model of self-avoiding manifolds, we study the effects of introducing random crosslinks between monomers on (in general) different manifolds. As for the case of linear polymers, one observes a continuous phase transition from a fluid to an amorphous solid state, characterized by a finite fraction of localized monomers We compute this fraction, as well as the typical localization length near the transition.