Geometry, Topology, and Universality of Random Surfaces
JAYANATH R. BANAVAR 1,
AMOS MARITAN 1, and
ATTILIO STELLA 2
1 Department of Physics and Materials Research Laboratory, The Pennsylvania State University, University Park, PA 16802
2 Dipartimento di Fisica, Universita di Bologna, 140126 Bologna, Italy, and Centro Interuniversitario Struttura della Materia, Universita di Padova, Padova 35131, Italy
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.
Submitted on December 18, 1990
Accepted on March 13, 1991
