Phase diagram of four-dimensional dynamical triangulations with a boundary

Abstract

We report on simulations of DT simplicial gravity for manifolds with the topology of the 4-disk. We find evidence for four phases in a two-dimensional parameter space. In two of these the boundary plays no dynamical role and the geometries are equivalent to those observed earlier for the sphere $S^4$. In another phase the boundary is maximal and the quantum geometry degenerates to a one dimensional branched polymer. In contrast we provide evidence that the fourth phase is effectively three-dimensional. We find discontinuous phase transitions at all the phase boundaries.

13 pages, latex

References in corpus (9)

• Focusing on the Fixed Point of 4D Simplicial Gravity
• Further evidence that the transition of 4D dynamical triangulation is 1st order
• Singular Vertices and the Triangulation Space of the D-sphere
• Singular Structure in 4D Simplicial Gravity
• Simulations of Dynamically Triangulated Gravity -- an Algorithm for Arbitrary Dimension
• Quantization of Geometry
• Three Dimensional Quantum Gravity Coupled to Ising Matter
• Monte Carlo Simulation of 2-D Quantum Gravity as Open Dynamically Triangulate Random Surfaces
• Phase diagram of three-dimensional dynamical triangulations with a boundary

Cited by in corpus (3)

• A first look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• A causal perspective on random geometry
• Birth and Growth of Two-dimensional Universe