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We study the phase diagram of a one-dimensional balls-in-boxes (BIB) modelthat has been proposed as an effective model for the spatial-volume dynamics of(2+1)-dimensional causal dynamical triangulations (CDT). The latter is astatistical model of random geometries and a candidate for a nonperturbativeformulation of quantum gravity, and it is known to have an interesting phasediagram, in particular including a phase of extended geometry with classicalproperties. Our results corroborate a previous analysis suggesting that aparticular type of potential is needed in the BIB model in order to reproducethe droplet condensation typical of the extended phase of CDT. Since such apotential can be obtained by a minisuperspace reduction of a (2+1)-dimensionalgravity theory of the Ho\v{r}ava-Lifshitz type, our result strengthens the linkbetween CDT and Ho\v{r}ava-Lifshitz gravity.

Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model