Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

TL;DR

This study investigates how boundary conditions influence the nature of the crumpling transition in a tethered membrane model with intrinsic curvature on spherical surfaces, revealing a change from first- to second-order transition depending on boundary vertex distance.

Contribution

It demonstrates that boundary vertex distance affects the order of the crumpling transition in an intrinsic curvature membrane model, a novel insight into boundary condition effects.

Findings

Transition order depends on boundary vertex distance

First-order transition becomes second-order with increased boundary distance

Monte Carlo simulations up to N=8412 used for analysis

Abstract

We found that the order for the crumpling transition of an intrinsic curvature model changes depending on the distance between two boundary vertices fixed on the surface of spherical topology. The model is a curvature one governed by an intrinsic curvature energy, which is defined on triangulated surfaces. It was already reported that the model undergoes a first-order crumpling transition without the boundary conditions on the surface. However, the dependence of the transition on such boundary condition is yet to be studied. We have studied in this paper this problem by using the Monte Carlo simulations on surfaces up to a size N=8412. The first-order transition changes to a second-order one if the distance increases.