The Crumpling Transition of Dynamically Triangulated Random Surfaces

TL;DR

This paper investigates the crumpling transition of dynamically triangulated random surfaces in 3D space, revealing topology-dependent critical behavior and a cusp singularity in specific heat through advanced simulations.

Contribution

It provides more accurate estimates of critical exponents and demonstrates topology dependence of the crumpling transition in dynamically triangulated surfaces.

Findings

Identification of a cusp singularity in specific heat

Topology influences transition temperature and exponents

Enhanced simulation data with longer runs

Abstract

We present the crumpling transition in three-dimensional Euclidian space of dynamically triangulated random surfaces with edge extrinsic curvature and fixed topology of a sphere as well as simulations of a dynamically triangulated torus. We used longer runs than previous simulations and give new and more accurate estimates of critical exponents. Our data indicate a cusp singularity in the specific heat. The transition temperature, as well as the exponents are topology dependent.