Euclidean Dynamical Triangulation revisited: is the phase transition really 1st order? (extended version)

Abstract

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [5,9]. However, one may wonder if this finding was affected by the numerical methods used: to control volume fluctuations, in both studies [5,9] an artificial harmonic potential was added to the action; in [9] measurements were taken after a fixed number of accepted instead of attempted moves which introduces an additional error. Finally the simulations suffer from strong critical slowing down which may have been underestimated. In the present work, we address the above weaknesses: we allow the volume to fluctuate freely within a fixed interval; we take measurements after a fixed number of attempted moves; and we overcome critical slowing down by using an optimized parallel tempering algorithm [12]. With these improved methods, on systems of size up to 64k 4-simplices, we confirm that the phase transition is first order. In addition, we discuss a local criterion to decide whether parts of a triangulation are in the elongated or crumpled state and describe a new correspondence between EDT and the balls in boxes model. The latter gives rise to a modified partition function with an additional, third coupling. Finally, we propose and motivate a class of modified path-integral measures that might remove the metastability of the Markov chain and turn the phase transition into second order.

26 pages, 21 figures, extended version of arXiv:1311.4712

References in corpus (2)

• Feedback-optimized parallel tempering Monte Carlo
• Optimized broad-histogram simulations for strong first-order phase transitions: Droplet transitions in the large-Q Potts model

Cited by in corpus (12)

• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Quantum gravity on foliated spacetime - asymptotically safe and sound
• Lattice Quantum Gravity and Asymptotic Safety
• Wicked metrics
• The de Sitter Instanton from Euclidean Dynamical Triangulations
• Spectrum of the Laplace-Beltrami Operator and the Phase Structure of Causal Dynamical Triangulation
• Locally Causal Dynamical Triangulations in Two Dimensions
• Convergence of Combinatorial Gravity
• Spectral Methods and Running Scales in Causal Dynamical Triangulations
• Derivation of the deformed Heisenberg algebra from discrete spacetime
• Yang-Lee zeros for real-space condensation
• Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations