Dependence of the surface tension on the shape of surface boundary

TL;DR

This study uses Monte Carlo simulations to demonstrate that membrane surface tension remains unaffected by the shape of the boundary surface, confirming this invariance in the thermodynamic limit for specific membrane models.

Contribution

It provides numerical evidence that surface tension is independent of boundary shape in membrane models, extending understanding of membrane physics.

Findings

Surface tension is shape-independent in the thermodynamic limit.

The invariance holds for Helfrich-Polyakov and Landau-Ginzburg models.

Monte Carlo simulations confirm theoretical predictions.

Abstract

We numerically check that the surface tension of membranes is independent of the shape of surface boundary. The surface tension is calculated by means of the Monte Carlo simulation technique on two types of cylinders made of rubans of size $L_1$ and $L_2$, where the rubans are the same for the projected area and different in the ratio $L_1/L_2$. The difference of the surface tension disappears in the thermodynamic limit in both models of Helfrich-Polyakov and Landau-Ginzburg.