Second-Order Phase Transition in Causal Dynamical Triangulations

Causal dynamical triangulations are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially be used to define a continuum limit in the conventional sense of nongravitational lattice theories.

Figure 1

The phase diagram of CDT. The large crosses represent actual measurements.

Figure 2

Measuring the location ${\Delta }^c$ of $B\mathrm{\text{−}}C$ transition points at ${\kappa }_0=2.2$ for different system sizes $N_4$ to determine the shift exponent $\tilde{\nu }$.

Figure 3

Dependence of the minimum of the Binder cumulant $B_{\mathrm{conj}(\Delta )}$ on the (inverse) system size at the $B\mathrm{\text{−}}C$ transition. At a second-order transition, $B^{\min }\to 0$ in the infinite-volume limit. (Fit excludes the two points on the right.)