Monte Carlo simulations of a tethered membrane model on a disk with intrinsic curvature

Abstract

A first-order phase transition separating the smooth phase from the crumpled one is found in a fixed connectivity surface model defined on a disk. The Hamiltonian contains the Gaussian term and an intrinsic curvature term.

Phase transitions of a tethered membrane model on a torus with intrinsic curvature

“…Relatively smaller number of MCS (0.8 × 10 8 ∼ 1.5 × 10 8 ) is iterated in the crumpled phase, because if the surfaces become once crumpled they hardly return smooth. This irreversibility was also seen in the model on a sphere [23] and in the model on a disk [24].…”

“…The shape of surfaces can be strongly influenced by intrinsic curvatures. Recently several numerical studies have been made on the phase diagram of the model with intrinsic curvature [23,24]. It was reported that the model undergoes a first-order phase transition between the smooth phase and the crumpled phase on a sphere [23] and on a disk [24].…”

Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

“…The model was known as the one that undergoes a first-order crumpling transition without the boundary condition [39,40,41]. This paper aimed to show how boundary conditions influence the phase transition, and we performed extensive MC simulations on the spherical tethered surfaces up to a size N = 8412.…”

“…It has been shown that the first-order transition can be seen in spherical fluid/tethered surfaces [38,39], tethered surface of disk topology [40], and tethered surface with torus topology [41].…”

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

“…Tethered surface models are defined on triangulated fixed connectivity surfaces representing polymerized biological membranes or membranes in the gel phase [7], and they are classified into a major class of the HPK model [15,16,17,18,19,20,21,22,23,24,25,26]. Fluid surface models are considered a different class of the HPK model defined on dynamically triangulated surfaces representing these biological membranes in the fluid phase, however, we will not discuss the fluid surface model in this paper [27,28,29,30,31,32,33,34].…”