The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs

TL;DR

This paper investigates the fractal properties and critical behavior of the Ising model on c=-5 gravity graphs generated by coupling a conformal field theory to 2D quantum gravity, confirming theoretical predictions.

Contribution

It provides the first numerical analysis of the Ising model on c=-5 gravity graphs, linking fractal geometry to critical phenomena in quantum gravity contexts.

Findings

Measured fractal dimensions consistent with theoretical predictions

Confirmed Ising critical behavior matches coupled gravity models

Suggested geometry determines critical behavior, not coupling details

Abstract

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 gamma_s and the intrinsic fractal dimensions d_H. We find gamma_s = -1.5(1) and d_H = 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.