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 $\epsilon \in (0,1]$. 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 ${\beta }_c^{-1}$ decreases monotonotically with $\epsilon$. The line of phase transitions in the ${\beta }_c^2$ v/s $\epsilon$ plane asymptotes to the infinite temperature axis, suggesting that the continuum phase survives the analytic continuation.

14 pages, 13 figures

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