Issues of replica-symmetry breaking for the amorphous solid state of vulcanized macromolecules

The statistical mechanics of vulcanized (i.e. permanently randomly crosslinked) macromolecular matter can be formulated, using the replica technique, as the n to 0 limit of a theory containing n+1 coupled replicas. Within the framework of a replica-symmetric variational mean-field approach, this theory describes an equilibrium phase transition, upon sufficient vulcanization, from a liquid to an amorphous solid state. We consider a natural extension of this framework, which admits the possibility of the spontaneous breaking of replica symmetry, and find that-at least at the mean-field level-replica symmetry appears to remain intact. We discuss the physical origin of this absence of replica-symmetry breaking, as well as a possible strategy for a theoretical refinement that may yield replica-symmetry breaking.