Universality Classes of Self-Avoiding Crystalline Membranes
Abstract
We present an analysis of extensive large-scale Monte Carlo simulations of self-avoiding crystalline membranes for sizes (number of faces) ranging from 512 to 17672 (triangular) plaquettes. Self-avoidance is implemented via impenetrable plaquettes. We 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 crystalline membranes -- the roughness exponent in three dimensions is xi=0.63(4). This suggests that there is a unique universality class for flat crystalline membranes without attractive interactions. To investigate bulk dimensions above four we generalize the plaquette model to the self-avoiding solid-on-solid (SASOS) model and discuss its properties. Finally we address some theoretical and experimental implications of our work.Keywords
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