IN-PLANE DEFORMATION OF A TRIANGULATED SURFACE MODEL WITH METRIC DEGREES OF FREEDOM

Abstract

Using the canonical Monte Carlo simulation technique, we study a Regge calculus model on triangulated spherical surfaces. The discrete model is statistical mechanically defined with the variables X, g and ρ, which denote the surface position in R3, the metric on a two-dimensional surface M and the surface density of M, respectively. The metric g is defined only by using the deficit angle of the triangles in M. This is in sharp contrast to the conventional Regge calculus model, where g depends only on the edge length of the triangles. We find that the discrete model in this paper undergoes a phase transition between the smooth spherical phase at b → ∞ and the crumpled phase at b → 0, where b is the bending rigidity. The transition is of first-order and identified with the one observed in the conventional model without the variables g and ρ. This implies that the shape transformation transition is not influenced by the metric degrees of freedom. It is also found that the model undergoes a continuous transition of in-plane deformation. This continuous transition is reflected in almost discontinuous changes of the surface area of M and that of X(M), where the surface area of M is conjugate to the density variable ρ.