Evidence for a Phase Transition in 2D Causal Set Quantum Gravity

Abstract

We present evidence for a phase transition in a theory of 2D causal set quantum gravity which contains a dimensionless non-locality parameter $ε\in (0,1]$. The transition is between a continuum phase and a crystalline phase, characterised by a set of covariant observables. For a fixed size of the causal set the transition temperature $β_c^{-1}$ decreases monotonotically with $ε$. The line of phase transitions in the $β_c^2$ v/s $ε$ plane asymptotes to the infinite temperature axis, suggesting that the continuum phase survives the analytic continuation.

14 pages, 13 figures