Minimal Dynamical Triangulations of Random Surfaces

Abstract

We introduce and investigate numerically a minimal class of dynamical triangulations of two-dimensional gravity on the sphere in which only vertices of order five, six or seven are permitted. We show firstly that this restriction of the local coordination number, or equivalently intrinsic scalar curvature, leaves intact the fractal structure characteristic of generic dynamically triangulated random surfaces. Furthermore the Ising model coupled to minimal two-dimensional gravity still possesses a continuous phase transition. The critical exponents of this transition correspond to the usual KPZ exponents associated with coupling a central charge c=1/2 model to two-dimensional gravity.

Latex, 9 pages, 3 figures, Published version

References in corpus (5)

• On the fractal structure of two-dimensional quantum gravity
• Exact Solution of Discrete Two-Dimensional R^2 Gravity
• Scaling and the Fractal Geometry of Two-Dimensional Quantum Gravity
• A Real-Space Renormalization Group for Random Surfaces
• A geometric approach to free variable loop equations in discretized theories of 2D gravity

Cited by in corpus (9)

• Uniform Infinite Planar Triangulations
• Simulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations
• The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs
• Freezing of Triangulations
• Three-Dimensional Simplicial Gravity and Degenerate Triangulations
• Random Surfaces and Lattice Gravity
• Curvature Matrix Models for Dynamical Triangulations and the Itzykson-DiFrancesco Formula
• Gravity and Random Surfaces on the Lattice - A Review
• Kertesz on Fat Graphs?