Phase structure of intrinsic curvature models on dynamically triangulated disk with fixed boundary length

TL;DR

This study investigates phase transitions in intrinsic curvature models on dynamically triangulated disks, revealing that the phase structure is similar to that of spherical surfaces and independent of surface closure.

Contribution

It demonstrates that the phase structure of fluid surface models with intrinsic curvature is consistent between open disks and closed spheres.

Findings

First-order phase transition between smooth and non-smooth phases

Existence of a crumpled phase at low curvature coefficient

Phase structure is topology-independent

Abstract

A first-order phase transition is found in two types of intrinsic curvature models defined on dynamically triangulated surfaces of disk topology. The intrinsic curvature energy is included in the Hamiltonian. The smooth phase is separated from a non-smooth phase by the transition. The crumpled phase, which is different from the non-smooth phase, also appears at sufficiently small curvature coefficient $\alpha$. The phase structure of the model on the disk is identical to that of the spherical surface model, which was investigated by us and reported previously. Thus, we found that the phase structure of the fluid surface model with intrinsic curvature is independent of whether the surface is closed or open.