Mitsuru Yamada

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.

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

A first-order phase transition separating the smooth phase from the crumpled one is found in a fixed connectivity surface model defined on a disk. The Hamiltonian contains the Gaussian term and an intrinsic curvature term.

PHASE TRANSITION OF A MODEL OF FLUID MEMBRANE

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.

Phase Transition Of A Model Of Crystalline Membrane

We study two-dimensional triangulated surfaces of sphere topology by the canonical Monte Carlo simulation. The coordination number of surfaces is made as uniform as possible. The triangulation is fixed in MC so that only the positions X of vertices may be considered as the dynamical variable. The well-known Helfrich energy function S = S1 + bS2 is used for the definition of the model where S1 and S2 are the area and bending energy functions respectively and b is the bending rigidity. The discretizations of S1 and S2 are identical with that of our previous MC study for a model of fluid membranes. We find that the specific heats have peaks at finite bending rigidities and obtain the critical exponents of the phase transition by the finite-size scaling technique. It is found that our model of crystalline membranes undergoes an expected second order phase transition.

STATISTICAL MECHANICS OF A RIGID BUBBLE: HIGHER DERIVATIVE QUANTUM GRAVITY ON A SPHERICAL RANDOM SURFACE EMBEDDED IN E3

A model of rigid surface of S2 topology embedded in a three-dimensional Euclidean space E3 is numerically studied. The action of the model has an extrinsic curvature term SEC in addition to the two-dimensional higher derivative gravity action. Since the SEC is thought of as the correlation energy of the normal vectors of the surface, it is discretized by an analogy to the σ model. The expected ideal gas behavior of the model can be seen from the Monte Carlo results at sufficiently low temperatures. The phase structure of the model is investigated and it is found that the SEC in the action causes some phase transition at an intermediate temperature.

A Monte Carlo Study of Two-dimensional Higher Derivative Quantum Gravity on a Triangulated Random Surface

A new form of curvature on a 2-dimensional Regge manifold is proposed and the higher derivative quantum gravity is studied numerically by use of both a fixed and a random coordination number lattice. Results previously reported by Hamber and Williams are followed. Also checked are the stability and the absence of phase transition of the theory whose action has a cosmological term and an R2 term.

OPERATOR ORDERING AND CLASSICAL SOLITON PATH IN TWO-DIMENSIONAL N = 2 SUPERSYMMETRY WITH KÄHLER POTENTIAL

We investigate a two-dimensional N = 2 supersymmetric model which consists of n chiral superfields with Kahler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super-Poincare algebra by carrying out the canonical Dirac bracket quantization. This is shown to be also true when the supersymmetry algebra has a central extension by the presence of topological soliton. It is also shown that the path of soliton is a straight line in the complex plane of superpotential W and triangular mass inequality holds. One half of supersymmetry is broken by the presence of soliton.

OPERATOR ORDERING IN TWO-DIMENSIONAL N = 1 SUPERSYMMETRY WITH CURVED MANIFOLD

We investigate an operator ordering problem in two-dimensional N = 1 supersymmetric model which consists of n real superfields. There arises an operator ordering problem when the target space is curved. We have to fix the ordering in quantum operator properly to obtain the correct supersymmetry algebra. We demonstrate that the super-Poincare algebra fixes the correct operator ordering. We obtain a supercurrent with correct operator ordering and a central extension of supersymmetry algebra.

A MONTE CARLO STUDY OF THE O(3) sigma MODEL ON A CURVED RANDOM SURFACE

The O(3) σ-model is studied numerically on a curved random surface, which is constructed from a flat random lattice by the change of each link length. The pair correlation, the specific heat and the magnetic susceptibility are calculated. It is shown that the continuum limit of the model can be obtained when the curvature is reasonably small.

Holonomy and lattice simulation of topologically non-trivial gauge fields

The holonomy of a gauge configuration is calculated from the transition function and the path-ordered exponential of the gauge potential for the case of general base manifolds. A general rule for the lattice simulation of gauge fields is proposed by explicitly giving the link variables. It is applied to a cold-start Monte Carlo study of the U(1) gauge field on a torus and the average energy of a definite topological configuration is calculated.