Shape transformations of a model of self-avoiding triangulated surfaces of sphere topology

TL;DR

This study investigates how self-avoidance influences phase behavior in a triangulated surface model with sphere topology, revealing minimal impact on phase variety but preventing crumpling at zero pressure.

Contribution

It introduces a self-avoiding interaction into a fixed-connectivity surface model and analyzes its effects on phase structure under different pressure conditions.

Findings

Self-avoidance minimally affects phase variety.

No crumpled surface appears at zero pressure.

Hausdorff dimension differs from previous SA models.

Abstract

We study a surface model with a self-avoiding (SA) interaction using the canonical Monte Carlo simulation technique on fixed-connectivity (FC) triangulated lattices of sphere topology. The model is defined by an area energy, a deficit angle energy, and the SA potential. A pressure term is also included in the Hamiltonian. The volume enclosed by the surface is well defined because of the self-avoidance. We focus on whether or not the interaction influences the phase structure of the FC model under two different conditions of pressure ${\it \Delta} p$; zero and small negative. The results are compared with the previous results of the self-intersecting model, which has a rich variety of phases; the smooth spherical phase, the tubular phase, the linear phase, and the collapsed phase. We find that the influence of the SA interaction on the multitude of phases is almost negligible except for the evidence that no crumpled surface appears under ${\it \Delta} p\=\0$ at least even in the limit of zero bending rigidity $\alpha\to \0$. The Hausdorff dimension is obtained in the limit of $\alpha\to \0$ and compared with previous results of SA models, which are different from the one in this paper.