Phase transition of triangulated spherical surfaces with elastic skeletons

TL;DR

This study numerically demonstrates a first-order phase transition in a spherical surface model with elastic skeletons, showing shape changes from swollen to crumpled states driven by bending rigidity.

Contribution

It introduces a novel model of spherical surfaces with elastic skeletons exhibiting a first-order phase transition, highlighting the role of skeleton elasticity in membrane shape stability.

Findings

Identified a first-order transition between swollen and crumpled phases.

Showed the influence of skeleton bending rigidity on surface shape.

Indicated relevance to biological membranes with cytoskeletons.

Abstract

A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of the triangulated surfaces is maintained by skeletons, which have a one-dimensional bending elasticity characterized by the bending rigidity $b$, and the surfaces have no two-dimensional bending elasticity except at the junctions. The surfaces swell and become spherical at large $b$ and collapse and crumple at small $b$. These two phases are separated from each other by the first-order transition. Although both of the surfaces and the skeleton are allowed to self-intersect and, hence, phantom, our results indicate a possible phase transition in biological or artificial membranes whose shape is maintained by cytoskeletons.