Nobuyuki Kusano

First-order phase transition of fixed connectivity surfaces.

We report 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. One 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 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.

Phase transition of surface models with intrinsic curvature

Abstract.It is reported that a surface model of Polyakov strings undergoes a first-order phase transition between smooth and crumpled (or branched polymer) phases. The Hamiltonian of the model contains the Gaussian term and a deficit angle term corresponding to the weight of the integration measure dX in the partition function.

Non-vanishing string tension of elastic membrane models

Abstract By using the grand canonical Monte Carlo simulations on spherical surfaces with two fixed vertices separated by the distance L, we find that a second-order phase transition changes to a first-order one when L is sufficiently large. We find that string tension σ ≠ 0 in the smooth phase while σ → 0 in the wrinkled phase.

Monte Carlo simulations of tensionless membranes

Abstract We study tensionless models of crystalline membranes and fluid membranes on triangulated surfaces of spherical topology. The Hamiltonian contains a bending energy and a hard wall potential. We find that a phase transition of shape fluctuation seen in the crystalline model is softened by the fluidity of lateral diffusion of vertices.

String Tension and Surface Tension of Elastic Membranes with Fluidity

The string tension and the surface tension of a model of elastic and phantom membranes are calculated by the grand canonical Monte Carlo simulation. It is shown by scaling arguments that both of them vanish at the critical point of the phase transition.