First-order phase transition of triangulated surfaces on a spherical core

TL;DR

This study uses Monte Carlo simulations to analyze a curvature model on triangulated surfaces with a spherical core, revealing a first-order shape transition influenced by core size, with implications for biological membranes.

Contribution

It demonstrates a first-order shape transition in a triangulated surface model with a spherical core, highlighting the role of core size and state degeneracy.

Findings

Discontinuous shape transition between smooth and collapsed states.

Transition depends on the core radius R.

Discontinuous change in Gaussian bond potential S_1/N at transition.

Abstract

We study an intrinsic curvature model defined on fixed-connectivity triangulated lattices enclosing a spherical core by using the canonical Monte Carlo simulation technique. We find that the model undergoes a discontinuous transition of shape transformation between the smooth state and a collapsed state even when the core radius $R$ is sufficiently large; the transition depends on $R$. The origin of the multitude of transitions is considered to be a degeneracy of the collapsed states. We also find that the Gaussian bond potential $S_1/N$, which is the sum of bond length squares, discontinuously changes at the transition. The discontinuity in $S_1/N$ implies a possibility of large fluctuations of the distance between lipids, or the density of lipids, in biological membranes such as giant vesicles or liposomes enclosing some materials.