Anisotropic scaling of tethered self-avoiding membranes

Extensive Monte Carlo simulations are reported of a model for tethered membranes that includes bending rigidity and self-avoidance. These simulations are performed over a range of temperature and for embedding dimensions d=3, 4, and 5. The membranes have a stretched configuration that is hexagonal with linear dimension L in the range 5--25. The equilibrium shape of the membranes is analyzed by calculating the eigenvalues of the inertia tensor as well as structure factors S(k) with k in the direction of the eigenvectors of this tensor. The eigenvalues and structure factor show a scaling behavior which indicates that in the thermodynamic limit the membranes are flat rather than crumpled for all temperatures and particle diameters, except possibly in the very weak self-avoidance limit, similar to the ``phantom'' membrane (one in which particles that are not nearest neighbors on the network do not interact, i.e., they can pass through each other).