Geometry, Topology, and Universality of Random Surfaces

Science  10 May 1991:
Vol. 252, Issue 5007, pp. 825-827
DOI: 10.1126/science.252.5007.825


Previous simulations of a self-avoiding, closed random surface with restricted topology (without handles) on a three-dimensional lattice have shown that its behavior on long length scales is consistent with that of a branched-polymer. It is shown analytically that such a surface with an unrestricted number of handles has a qualitatively different geometry and therefore is in a different universality class. The effect of a net external pressure is to suppress the handles and collapse the surface into a branched polymer-like configuration. Topology is thus shown to be a key factor in determining the universality class of the system.

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