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Self-Avoiding Random Surfaces: Monte Carlo Study Using Oct-tree Data- structures



John O'Connell, F Sullivan, Donald E. Libes, E Orlandini, M Tesi, A Stella, T L. Einstein


Self-avoiding random surfaces on a cubis lattice are studied by extensive Monte Carlo sampling. The surfaces have empty boundary and the topology of a 2-sphere. An oct-tree data structure allows good statistics to be obtained for surfaces whose plaquette number is up to an order of magnitude greater than in previous investigations. The new simulation strategy is explained in detail and compared with previous ones. The critical plaquette fugacity, -1, and the entropic exponent, 0, are determined by maximum likelihood methods and by logarithmic plots of the average surface area versus fugacity. The latter approach, which produces results having much better convergence by taking advantage of the scaling properties of several runs at various fugacities, leads to the estimates = 1.729 0.036 and 0 = 1.500 0.026. Linear regression estimates for the radius of gyration exponent give = 0.509 0.004, while the asymptotic ratio of surface area over average volume enclosed approaches a finite value of 3.18 0.03. Our results give strong corroborating evidence that this long-controversial problem belongs to the universality class of branched polymers.
The Journal of Physics


cubis lattice, data structure, Monte Carlo Study, self-avoiding random surfaces, sphere


O'Connell, J. , Sullivan, F. , Libes, D. , Orlandini, E. , Tesi, M. , Stella, A. and Einstein, T. (1991), Self-Avoiding Random Surfaces: Monte Carlo Study Using Oct-tree Data- structures, The Journal of Physics, [online], (Accessed April 19, 2024)
Created June 30, 1991, Updated October 12, 2021