Two-Dimensional 8-State Potts Model on Random Lattices: A Monte Carlo Study

TL;DR

This study uses Monte Carlo simulations on random lattices to investigate how quenched coordination number randomness affects the phase transition in the eight-state Potts model, finding it remains first order unlike other types of randomness.

Contribution

It provides new evidence that quenched coordination randomness does not change the first-order transition in the 8-state Potts model, contrasting previous findings with bond randomness.

Findings

Phase transition remains first order with quenched coordination randomness.

Contrasts with previous studies showing transition changes with bond randomness.

Supports robustness of first-order transition under certain types of quenched disorder.

Abstract

We use two-dimensional Poissonian random lattices of Voronoi/ Delaunay type to study the effect of quenched coordination number randomness on the nature of the phase transition in the eight-state Potts model, which is of first order on regular lattices. From extensive Monte Carlo simulations we obtain strong evidence that the phase transition remains first order for this type of quenched randomness. Our result is in striking contrast to a recent Monte Carlo study of quenched bond randomness for which the order of the phase transition changes from first to second order.