First-order phase transition in the tethered surface model on a sphere

TL;DR

This study demonstrates a first-order phase transition in the tethered surface model on a sphere, with transition order depending on surface size, confirmed through extensive Monte Carlo simulations.

Contribution

It provides the first large-scale simulation evidence of a first-order transition in the tethered surface model on spherical surfaces.

Findings

First-order transition observed for N>7000

Continuous transition on smaller surfaces

Results align with previous phase structure studies

Abstract

We show that the tethered surface model of Helfrich and Polyakov-Kleinert undergoes a first-order phase transition separating the smooth phase from the crumpled one. The model is investigated by the canonical Monte Carlo simulations on spherical and fixed connectivity surfaces of size up to N=15212. The first-order transition is observed when N>7000, which is larger than those in previous numerical studies, and a continuous transition can also be observed on small-sized surfaces. Our results are, therefore, consistent with those obtained in previous studies on the phase structure of the model.