Grand canonical simulations of string tension in elastic surface model

Abstract

Abstract. We report a numerical evidence that the string tension σ can be viewed as an order parameter of the phase transition, which separates the smooth phase from the crumpled one, in the fluid surface model of Helfrich and Polyakov-Kleinert. The model is defined on spherical surfaces with two fixed vertices of distance L. The string tension σ is calculated by regarding the surface as a string connecting the two points. We find that the phase transition strengthens as L is increased, and that σ vanishes in the crumpled phase and non-vanishes in the smooth phase.PACS. 64.60.-i General studies of phase transitions -68.60.-p Physical properties of thin films, nonelectronic -87.16.Dg Membranes, bilayers, and vesicles

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

“…We will find that the order of the transition changes from first-order to second-order and higher-orders in the limit of N → ∞ when L(N) is increased from L 0 (N) to 1.5L 0 (N) and 2L 0 (N), respectively, where L 0 (N) is a radius of the initial sphere such that the Gaussian energy S 1 /N is approximately equal to S 1 /N ∼ 3/2 at the start of MC simulations. The result in this paper is in sharp contrast to that of the fluid surface model with extrinsic curvature, where the phase transition is strengthened with the increasing L(N) [31,32].…”

“…The surface models can be classified into two groups, which are characterized by the curvature energy in the Hamiltonian; one is an extrinsic curvature model [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32], and the other is an intrinsic curvature model [33,34,35,36]. The extrinsic curvature model is known to undergo a first-order transition between the smooth phase and the crumpled phase on tethered spherical surfaces [22,23,24].…”

Phase Transition of Triangulated Spherical Surfaces with Elastic Skeletons

“…Therefore it is interesting to see whether the crumpling transition occurs in such skeleton surface models. The transition is the one that has long been studied theoretically [11,12,13] and numerically [14,15,16,17,18,19,20,21] on the basis of the HPK model, and an experimental investigation on the transition has also been performed recently [2].…”

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]. …”