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

Abstract

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.