Nonvanishing string tension of elastic membrane models

TL;DR

This study uses grand canonical Monte Carlo simulations to investigate phase transitions in elastic membrane models on spherical surfaces, revealing a change from second-order to first-order transitions and demonstrating non-zero string tension in the smooth phase.

Contribution

It shows how the order of phase transitions in elastic membranes depends on the separation distance, and identifies non-zero string tension in the smooth phase.

Findings

Transition changes from second-order to first-order at large L

String tension remains non-zero in the smooth phase

String tension approaches zero in the wrinkled phase

Abstract

By using the grand canonical Monte Carlo simulations on spherical surfaces with two fixed vertices separated by the distance L, we find that the second-order phase transition changes to the first-order one when L is sufficiently large. We find that string tension \sigma \not= 0 in the smooth phase while \sigma \to 0 in the wrinkled phase.