Tethered Membranes with Quenched Random Internal Disorders and Long Range Interactions

Abstract

In the large limit of the embedding space dimension d, D-dimensinal tethered membranes are studied. Quenched disorders in the internal preferred metric and the spontaneous curvature, and long range repulsive interactions which fall off with distance r like 1⁄r^γ are assumed. The flat phase is unstable due to the disorder of the metric and the spin-glass phase takes over as in the phantom randomly polymerized membrane case. A complete phase diagram in the (γ, D) plane is obtained. The crumpled phase of the membranes is not affected by the randomnesses and the existence region remains the same. The exact exponent for the radius of gyration in the spin-glass phase is given. From a comparison with the crumpling transition in the self-avoiding tethered membrane, we propose a conjecture that the wrinkling transition dose not exist in the self-avoiding randomly polymerized membrane.