Excluded-volume interactions in tethered membranes

The Monte Carlo method is applied to investigate the asymptotic behavior of self-avoiding polymerized membranes. We use a model described by a local Hamiltonian: repulsive interactions (hard spheres of diameter σ) act only between atoms whose degree of neighborhood (measured along the membrane) does not exceed a certain value l. For a particular value σ=σc(l) the membrane undergoes a crumpling transition between asymptotically flat and crumpled states. We find that when l increases, σc(l) decays to zero, and conclude that self-avoiding surfaces with purely repulsive interactions are asymptotically flat even for very small values of σ.