First-order phase transition of fixed connectivity surfaces

Abstract

We report a numerical evidence of the discontinuous transition of a tethered membrane model which is defined within a framework of the membrane elasticity of Helfrich. Two kinds of phantom tethered membrane models are studied via the canonical Monte Carlo simulation on triangulated fixed connectivity surfaces of spherical topology. A surface model is defined by the Gaussian term and the bending energy term, and the other, which is tensionless, is defined by the bending energy term and a hard wall potential. The bending energy is defined by using the normal vector at each vertex. Both of the models undergo the first-order phase transition characterized by a gap of the bending energy. The phase structure of the models depends on the choice of discrete bending energy.

Universal behavior of crystalline membranes: Crumpling transition and Poisson ratio of the flat phase

“…Refs. [20] (with a arXiv:1511.08615v2 [cond-mat.stat-mech] 5 Feb 2016 truncated Lennard-Jones potential) and [21][22][23] (spherical topology). Results from non-perturbative renormalization group (RG) calculations are in agreement with these [24].…”

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].…”

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

“…It has been recognized that the phantom tethered model undergoes a second-order phase transition both on a sphere [20,21,22,23,24,25,26,27,28] and on a disk [29,30]. On the other hand, it has also been reported that there is a first-order transition in the model with Hamiltonian slightly different from the ordinary one of Helfrich and Polyakov-Kleinert on a sphere [25]. First-order transitions can also be seen in a model of Nambu-Goto Hamiltonian with a deficit angle term [26] and in a model with Hamiltonian containing the Gaussian term and an intrinsic curvature term [20].…”

“…Models on triangulated surfaces can be classified into two groups. One of them is the fluid model which is defined on dynamical connectivity surfaces [13,14,15,16,17,18,19,20], and the other is the tethered model on fixed connectivity surfaces [20,21,22,23,24,25,26,27,28,29,30]. There is another classification of surface models; a model is called real or phantom according to whether the surface is self-avoiding or not.…”