Crumpling transition in polymerized membranes

Abstract

The effect of a finite bending rigidity \ensuremath{\kappa}' on flexible, polymerized surfaces without self-avoidance is studied via the Monte Carlo method. Unlike linear polymers or liquid membranes, these surfaces undergo a remarkable finite-temperature crumpling transition, with a diverging specific heat. For small \ensuremath{\kappa}'/${\mathrm{k}}_{\mathrm{B}}$T, the surface is crumpled, and the radius of gyration ${\mathrm{R}}_{\mathrm{G}}$ grows as ln${\mathrm{L}}^{1/2}$, where L is the linear size of uncrumpled membrane. For large \ensuremath{\kappa}'/${\mathrm{k}}_{\mathrm{B}}$T, we find that the surface remains flat, i.e., ${\mathrm{R}}_{\mathrm{G}}$\ensuremath{\sim}L. Our results strongly suggest a finite-temperature crumpling transition in polymerized self-avoiding membranes as well.