RANDOM NETWORKS OF CROSS-LINKED MANIFOLDS

We generalize the statistical mechanical theory of vulcanization to th e case of D-dimensional polymerized manifolds. Starting from a continu um model of self-avoiding manifolds, we study the effects of introduci ng random crosslinks between monomers on (in general) different manifo lds. As for the case of linear polymers, one observes a continuous pha se 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.