First-order phase transition of the tethered membrane model on spherical surfaces

TL;DR

This paper demonstrates that various tethered membrane models, including Helfrich, Polyakov, Kleinert, Nambu, and Goto, all exhibit a first-order phase transition between smooth and crumpled states, indicating universality across discretizations.

Contribution

It shows that the first-order phase transition in tethered membrane models is universal, regardless of the specific discretization of the Hamiltonian.

Findings

All models undergo a first-order transition.

Transition is independent of Hamiltonian discretization.

Results apply to biological membranes and vesicles.

Abstract

We found that three types of tethered surface model undergo a first-order phase transition between the smooth and the crumpled phase. The first and the third are discrete models of Helfrich, Polyakov, and Kleinert, and the second is that of Nambu and Goto. These are curvature models for biological membranes including artificial vesicles. The results obtained in this paper indicate that the first-order phase transition is universal in the sense that the order of the transition is independent of discretization of the Hamiltonian for the tethered surface model.