# Softening of First-Order Phase Transition on Quenched Random Gravity Graphs

## TL;DR

This study uses Monte Carlo simulations to show that quenched randomness in 2D gravity graphs softens the 10-state Potts model's first-order phase transition to a continuous one, indicating a new universality class.

## Contribution

It provides the first numerical evidence that quenched coordination number randomness can change a first-order phase transition into a continuous one in gravity graphs.

## Key findings

- Quenched randomness softens the phase transition from first to continuous.
- Results suggest a new universality class for the transition.
- Contrasts with Poissonian random lattices where the transition remains first order.

## Abstract

We perform extensive Monte Carlo simulations of the 10-state Potts model on quenched two-dimensional $\Phi^3$ gravity graphs to study the effect of quenched coordination number randomness on the nature of 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, representing presumably a new universality class. This result is in striking contrast to a recent Monte Carlo study of the 8-state Potts model on two-dimensional Poissonian random lattices of Voronoi/Delaunay type, where the phase transition clearly stayed of first order, but is in qualitative agreement with results for quenched bond randomness on regular lattices. A precedent for such softening with connectivity disorder is known: in the 10-state Potts model on annealed Phi3 gravity graphs a continuous transition is also observed.