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 dimension 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, with a total central charge of the matter sector c=−5.