Surface tension in an intrinsic curvature model with fixed one-dimensional boundaries

TL;DR

This study uses Monte Carlo simulations to explore how intrinsic curvature affects surface tension and phase transitions in a fixed boundary triangulated surface model, revealing a first-order transition with discontinuous changes in surface tension.

Contribution

It introduces a fixed boundary condition in a triangulated surface model to analyze surface tension and phase transitions driven by intrinsic curvature.

Findings

Surface tension exhibits a discontinuous change at the transition.

The transition is of first-order with a constant tension gap.

Surface tension is nearly zero in the wrinkled phase and finite in the smooth phase.

Abstract

A triangulated fixed connectivity surface model is investigated by using the Monte Carlo simulation technique. In order to have the macroscopic surface tension \tau, the vertices on the one-dimensional boundaries are fixed as the edges (=circles) of the tubular surface in the simulations. The size of the tubular surface is chosen such that the projected area becomes the regular square of area A. An intrinsic curvature energy with a microscopic bending rigidity b is included in the Hamiltonian. We found that the model undergoes a first-order transition of surface fluctuations at finite b, where the surface tension \tau discontinuously changes. The gap of \tau remains constant at the transition point in a certain range of values A/N^\prime at sufficiently large N^\prime, which is the total number of vertices excluding the fixed vertices on the boundaries. The value of \tau remains almost zero in the wrinkled phase at the transition point while \tau remains negative finite in the smooth phase in that range of A/N^\prime.