Universality classes of self-avoiding fixed-connectivity membranes

We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding fixed-connectivity membranes for sizes (number of faces) ranging from 512 to. 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. T;Ve simulate the impenetrable plaquette model in both three and four bulk dimensions. In both cases we find the membrane to be flat for all temperatures: the size exponent in three dimensions is nu = 0.95(5) (Hausdorff dimension d(H) = 2.1(1)). The single flat phase appears, furthermore, to be equivalent to the large bending rigidity phase of non-self-avoiding fixed-connectivity membranes -the roughness exponent in three dimensions is xi = 0.63(4). This suggests that there is a unique universality class for flat fixed-connectivity membranes without attractive interactions. Finally, we address some theoretical and experimental implications of our work.