Softening Transitions with Quenched 2D Gravity

We perform extensive Monte Carlo simulations of the 10-state Potts model on quenched two-dimensional ${\mathrm{\Phi }}^3$ gravity graphs to study the effect of quenched connectivity disorder on the phase transition, which is strongly first order on regular lattices. The numerical data provides strong evidence that, due to the quenched randomness, the discontinuous first-order phase transition of the pure model is softened to a continuous transition.