Collapsing transition of spherical tethered surfaces with many holes

TL;DR

This study uses Monte Carlo simulations to analyze spherical tethered surfaces with many holes, revealing a first-order collapsing transition without surface fluctuation transition, where both phases remain smooth with Hausdorff dimension around 2.

Contribution

It demonstrates that surfaces with many holes exhibit only a collapsing transition at finite bending rigidity, differing from conventional models without holes.

Findings

First-order collapsing transition observed

No surface fluctuation transition detected

Both phases characterized by Hausdorff dimension ~2

Abstract

We investigate a tethered (i.e. fixed connectivity) surface model on spherical surfaces with many holes by using the canonical Monte Carlo simulations. Our result in this paper reveals that the model has only a collapsing transition at finite bending rigidity, where no surface fluctuation transition can be seen. The first-order collapsing transition separates the smooth phase from the collapsed phase. Both smooth and collapsed phases are characterized by Hausdorff dimension H\simeq 2, consequently, the surface becomes smooth in both phases. The difference between these two phases can be seen only in the size of surface. This is consistent with the fact that we can see no surface fluctuation transition at the collapsing transition point. These two types of transitions are well known to occur at the same transition point in the conventional surface models defined on the fixed connectivity surfaces without holes.