Phase Transition of a Model of Fluid Membrane

Abstract

A model of fluid membrane, which is not self-avoiding, such as two-dimensional spherical random surface is studied by using Monte Carlo simulation. Spherical surfaces in R3 are discretized by piecewise linear triangle. Dynamical variables are the positions X of the vertices and the triangulation g. The action of the model is sum of area energy and bending energy times bending rigidity b. The bending energy and the specific heat are measured, and the critical exponents of the phase transitions are obtained by a finite-size scaling technique. We find that our model of fluid membrane undergoes a second order phase transition.

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

“…In fact, it was reported recently that the Nambu-Goto model with a deficit angle term, which is an intrinsic curvature, is well-defined and undergoes a discontinuous transition between the smooth phase and a tubular phase [21]. The second model in this paper is also well-defined [31,19], because the Hamiltonian includes a bending energy, which is an extrinsic curvature defined according to the dual lattice formulation of the discrete mechanics by Lee [37].…”

“…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]. …”

Phase Transition of a Model of Crystalline Membrane

“…All of these are also different from those of fluid membrane model. 14 Figures 8(a) and 8(b) show the average square size,…”

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

“…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].…”