Grand Canonical simulations of string tension in elastic surface model

TL;DR

This paper provides numerical evidence that string tension acts as an order parameter distinguishing smooth and crumpled phases in a fluid surface model, with tension vanishing in the crumpled phase and non-zero in the smooth phase.

Contribution

It demonstrates that string tension can serve as an order parameter for phase transitions in elastic surface models, supported by grand canonical simulations.

Findings

String tension vanishes in the crumpled phase.

String tension is non-zero in the smooth phase.

Phase transition becomes more pronounced with increasing L.

Abstract

We report a numerical evidence that the string tension \sigma can be viewed as an order parameter of the phase transition, which separates the smooth phase from the crumpled one, in the fluid surface model of Helfrich and Polyakov-Kleinert. The model is defined on spherical surfaces with two fixed vertices of distance L. The string tension \sigma is calculated by regarding the surface as a string connecting the two points. We find that the phase transition strengthens as L is increased, and that \sigma vanishes in the crumpled phase and non-vanishes in the smooth phase.