Three-Dimensional Simplicial Gravity and Degenerate Triangulations

Abstract

I define a model of three-dimensional simplicial gravity using an extended ensemble of triangulations where, in addition to the usual combinatorial triangulations, I allow degenerate triangulations, i.e. triangulations with distinct simplexes defined by the same set of vertexes. I demonstrate, using numerical simulations, that allowing this type of degeneracy substantially reduces the geometric finite-size effects, especially in the crumpled phase of the model, in other respect the phase structure of the model is not affected.

Latex, 19 pages, 10 eps-figure

References in corpus (7)

• 4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields
• 4d Simplicial Quantum Gravity: Matter Fields and the Corresponding Effective Action
• Singular Structure in 4D Simplicial Gravity
• Singular Vertices in the Strong Coupling Phase of Four-Dimensional Simplicial Gravity
• Phase Structure of Dynamical Triangulation Models in Three Dimensions
• Multicanonical simulation of 3D dynamical triangulation model and a new phase structure
• Common Structures in Simplicial Quantum Gravity

Cited by in corpus (8)

• Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure Term
• De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation
• Simulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations
• Lattice Gravity and Random Surfaces
• Common Structures in Simplicial Quantum Gravity
• Simulating 4D Simplicial Gravity including Degenerate Triangulations
• The Weak-Coupling Limit of 3D Simplicial Quantum Gravity
• Phases of Tree-decorated Dynamical Triangulations in 3D