Evidence for the continuum in 2D causal set quantum gravity

We present evidence for a continuum phase in a theory of 2D causal set quantum gravity which contains a dimensionless non-locality parameter ɛ ∈ (0, 1]. We also find a phase transition between this continuum phase and a new crystalline phase which is characterized by a set of covariant observables. For a fixed size of the causal set, the transition temperature β^-1_c decreases monotonically with ɛ. The locus of the transition in the β² versus ɛ plane asymptotically approaches to the infinite temperature axis, suggesting that the continuum phase survives the analytic continuation.