Conformation of Self-Avoiding Randomly Tethered Membrane

Abstract

We report Monte-Carlo simulations of a model for a self-avoiding randomly tethered membrane. By changing the referencce bond length b, we have studied two cases of “weak” self-avoidance (b=3.0) and “strong” self-avoidance (b=1.7). The membrane with strong self-avoidance is asymptotically flat and its shrinkage is small as compared with the membrane without disorder. On the other hand, in contrast to our preliminary result [S. Mori, Phys. Lett. A 207 (1995) 87], the membrane with weak self-avoidance isin a crumpled phase with a large shrinkage. The exponent ν for the radius of gyration (R_G-- L^ν) is found to be ν=0.87 ± 0.02. We discuss the implications of the result, in particular its relevance to the understanding of the wrinkling transition in partially polymerized vesicles.