Phase transition of meshwork models for spherical membranes

TL;DR

This study investigates phase transitions in two types of spherical meshwork models using Monte Carlo simulations, revealing first-order collapsing transitions and differing surface fluctuation behaviors depending on junction elasticity.

Contribution

It introduces and compares two meshwork models with elastic and rigid junctions, analyzing their phase transition characteristics and surface fluctuation behaviors.

Findings

Both models exhibit first-order collapsing transitions.

The Hausdorff dimension in the smooth phase is approximately 2.

The first model shows a discontinuous surface fluctuation transition, while the second is continuous.

Abstract

We have studied two types of meshwork models by using the canonical Monte Carlo simulation technique. The first meshwork model has elastic junctions, which are composed of vertices, bonds, and triangles, while the second model has rigid junctions, which are hexagonal (or pentagonal) rigid plates. Two-dimensional elasticity is assumed only at the elastic junctions in the first model, and no two-dimensional bending elasticity is assumed in the second model. Both of the meshworks are of spherical topology. We find that both models undergo a first-order collapsing transition between the smooth spherical phase and the collapsed phase. The Hausdorff dimension of the smooth phase is H\simeq 2 in both models as expected. It is also found that H\simeq 2 in the collapsed phase of the second model, and that H is relatively larger than 2 in the collapsed phase of the first model, but it remains in the physical bound, i.e., H<3. Moreover, the first model undergoes a discontinuous surface fluctuation transition at the same transition point as that of the collapsing transition, while the second model undergoes a continuous transition of surface fluctuation. This indicates that the phase structure of the meshwork model is weakly dependent on the elasticity at the junctions.