Self-avoiding random surfaces with fluctuating topology

TL;DR

This paper explores a model of self-avoiding surfaces with variable topology, realized through a lattice system, and discusses their crumpling transition and relation to surface genus.

Contribution

It introduces a lattice realization of self-avoiding surfaces with polynomial curvature couplings and analyzes their topological and phase transition properties.

Findings

Mean surface area proportional to genus

Realization of surfaces in a 3D lattice with three local couplings

Discussion of crumpling transition and roughening phenomena

Abstract

A gas of self-avoiding surfaces with an arbitrary polynomial coupling to the gaussian curvature and an extrinsic curvature term can be realized in a three-dimensional Ising bcc lattice with only three local couplings. Similar three parameter realizations are valid also in other lattices. The relation between the crumpling transition and the roughening is discussed. It turns out that the mean area of these surfaces is proportional to its genus.