A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity?

We study matter with central charge $c >1$ coupled to two-dimensional (2d) quantum gravity, here represented as causal dynamical triangulations (CDT). 2d CDT is known to provide a regularization of (Euclidean) 2d Ho\v{r}ava-Lifshitz quantum gravity. The matter fields are massive Gaussian fields, where the mass is used to monitor the central charge $c$. Decreasing the mass we observe a higher order phase transition between an effective $c=0$ theory and a theory where $c>1$. In this sense the situation is somewhat similar to that observed for "standard" dynamical triangulations (DT) which provide a regularization of 2d quantum Liouville gravity. However, the geometric phase observed for $c >1$ in CDT is very different from the corresponding phase observed for DT.