Scaling behavior of the ising model coupled to two-dimensional quantum gravity

Abstract

We study the Ising model on dynamical ${\ensuremath{\varphi}}^{3}$ graphs with spherical topology. A finite-size scaling analysis is carried out both with and without an external field leading to numerical estimates for various critical exponents which are in good agreement with analytical calculations. We further determine the equation of state, and measure the correlation of Ising spins on the ensemble of graphs.