ISSUES OF REPLICA-SYMMETRY BREAKING FOR THE AMORPHOUS SOLID-STATE OF VULCANIZED MACROMOLECULES

The statistical mechanics of vulcanized (i.e. permanently randomly cro sslinked) macromolecular matter can be formulated, using the replica t echnique, as the n --> 0 limit of a theory containing n + 1 coupled re plicas. Within the framework of a replica-symmetric variational mean-f ield approach, this theory describes an equilibrium phase transition, upon sufficient vulcanization, from a liquid to an amorphous solid sta te. We consider a natural extension of this framework, which admits th e possibility of the spontaneous breaking of replica symmetry, and fin d that-at least at the mean-field level-replica symmetry appears to re main intact. We discuss the physical origin of this absence of replica -symmetry breaking, as well as a possible strategy for a theoretical r efinement that may yield replica-symmetry breaking.