Phase structure of a spherical surface model on fixed connectivity meshes

TL;DR

This paper studies a spherical surface model using Monte Carlo simulations, revealing a first-order collapsing transition and a continuous fluctuation transition, with surface shape maintained by a one-dimensional bending energy.

Contribution

It introduces a spherical surface model with a unique one-dimensional bending energy, analyzing phase transitions without two-dimensional bending energy.

Findings

Identifies a first-order collapsing transition.

Finds a continuous surface fluctuation transition.

Demonstrates shape stability via one-dimensional bending energy.

Abstract

An elastic surface model is investigated by using the canonical Monte Carlo simulation technique on triangulated spherical meshes. The model undergoes a first-order collapsing transition and a continuous surface fluctuation transition. The shape of surfaces is maintained by a one-dimensional bending energy, which is defined on the mesh, and no two-dimensional bending energy is included in the Hamiltonian.