Rigidity and ergodicity of randomly cross-linked macromolecules

We consider a system of randomly cross-linked, interacting macromolecules, within the framework of replica field theory. We find that above a critical number of cross links, translational and replica symmetry are simultaneously broken, thus showing that the system is an equilibrium amorphous solid, with many pure phases unrelated by global symmetry. We argue that each symmetry-unrelated pure phase describes a separate realization of the topology of the network.