First-order phase transition of fixed connectivity surfaces

TL;DR

This paper provides numerical evidence of a first-order phase transition in tethered membrane models based on Helfrich elasticity, showing how different energy definitions influence the phase structure.

Contribution

It demonstrates the first-order transition in two types of tethered membrane models using Monte Carlo simulations, highlighting the impact of discrete bending energy choices.

Findings

Both models exhibit a first-order phase transition with a discontinuous change in bending energy.

The phase structure varies depending on the discrete bending energy formulation.

Monte Carlo simulations effectively reveal the transition characteristics.

Abstract

We report a numerical evidence of the discontinuous transition of a tethered membrane model which is defined within a framework of the membrane elasticity of Helfrich. Two kinds of phantom tethered membrane models are studied via the canonical Monte Carlo simulation on triangulated fixed connectivity surfaces of spherical topology. A surface model is defined by the Gaussian term and the bending energy term, and the other, which is tensionless, is defined by the bending energy term and a hard wall potential. The bending energy is defined by using the normal vector at each vertex. Both of the models undergo the first-order phase transition characterized by a gap of the bending energy. The phase structure of the models depends on the choice of discrete bending energy.