The conformation and scaling properties of two-dimensional randomly triangulated self-avoiding surfaces embedded in three-dimensional space are studied using Monte Carlo methods. Results for the fractal dimension df and the spectral dimension dₛ, as well as the ratios of the eigenvalues of the moment of inertia tensor (which characterize the mean shapes of the surfaces), are presented. It is shown that these surfaces belong to the self-avoiding branched polymer universality class.
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D. M. Kroll (1992) studied this question.