Flat histogram Monte Carlo simulations of triangulated fixed-connectivity surface models

TL;DR

This paper demonstrates the successful application of the Wang-Landau flat histogram Monte Carlo method to study phase transitions in triangulated surface models, confirming first-order transitions and showcasing the method's effectiveness for large surface simulations.

Contribution

The study applies the FHMC technique to triangulated surface models with extrinsic curvature, confirming its applicability and effectiveness for large-scale surface simulations.

Findings

First-order surface fluctuation transition

First-order collapsing transition

FHMC technique is effective for large surface models

Abstract

Using the Wang-Landau flat histogram Monte Carlo (FHMC) simulation technique, we were able to study two types of triangulated spherical surface models in which the two-dimensional extrinsic curvature energy is assumed in the Hamiltonian. The Gaussian bond potential is also included in the Hamiltonian of the first model, but it is replaced by a hard-wall potential in the second model. The results presented in this paper are in good agreement with the results previously reported by our group. The transition of surface fluctuations and collapsing transition were studied using the canonical Metropolis Monte Carlo simulation technique and were found to be of the first-order. The results obtained in this paper also show that the FHMC technique can be successfully applied to triangulated surface models. It is non-trivial whether the technique is applicable or not to surface models because the simulations are performed on relatively large surfaces.