The Ising model on a Quenched Ensemble of c = −5 Gravity Graphs

We study with Monte Carlo methods an ensemble of c = −5 gravity graphs, generated by coupling a conformal field theory with central charge c = −5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent γs and the intrinsic fractal dimensions dH . We find γs = −1.5(1) and dH = 3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c = −5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, provided the total central charge of the matter sector is c = −5. From this we conjecture that the critical behavior of the Ising model is determined solely by the average fractal properties of the graphs, the coupling to the geometry not playing an important role.