Quenched Curvature Disorder in Polymerized Membranes

A model corresponding to the recently observed wrinkling transition in partially polymerized membranes is presented. In this model the quenched random internal disorder induced by the polymerization is coupled linearly to the local curvature of the membrane. It is argued that within the mean-field approximation the theory can be reduced to a Heisenberg spinglass with random Dzyaloshinsky-Moriya interactions. It exhibits crumpled, flat, spin-glass (and mixed) phases with a phase transition from the flat to the glass (or mixed) phase. It is argued that these conclusions should also hold for non-self-avoiding membranes in D = 2.