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

Abstract

We found that three types of tethered surface model undergo a first-order phase transition between the smooth and the crumpled phase. The first and the third are discrete models of Helfrich, Polyakov, and Kleinert, and the second is that of Nambu and Goto. These are curvature models for biological membranes including artificial vesicles. The results obtained in this paper indicate that the first-order phase transition is universal in the sense that the order of the transition is independent of discretization of the Hamiltonian for the tethered surface model.

Phase Transition of Triangulated Spherical Surfaces with Elastic Skeletons

“…It must be noted that a large surface in the collapsed phase hardly turns into the smooth phase even at the transition point. This phenomenon seems typical to surface simulations [16,17] based on the canonical MC simulation technique. When a large surface configuration is once trapped in a potential minimum, the configuration appears almost confined inside the potential valley.…”

“…5(a) and 5(b) that X 2 appears to remain unchanged as N increases in the crumpled phase. This implies that H is very large and is in contrast to that of the conventional tethered surface model in [16,17], where H is less than the physical bound in the crumpled phase. The phase transition is not reflected in the two-dimensional bending energy S J .…”

“…However, the two-dimensional S 1 seems to play no significant role in the transition, because a skeleton surface model with a one-dimensional bond potential also undergoes a phase transition [26]. It is expected that the skeleton surface model has a phase transition even without S 1 as in HPK model [17].…”

“…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].…”

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].…”