Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

TL;DR

This study uses microcanonical Monte Carlo simulations to test the Cardy-Jacobsen conjecture by analyzing the critical behavior of a three-dimensional site-diluted Potts model with eight states, confirming the conjecture's predictions.

Contribution

The paper provides the first precise numerical verification of the Cardy-Jacobsen conjecture for a three-dimensional Potts model with eight states at the tricritical point.

Findings

Critical exponents match those of the Random Field Ising Model

Transition changes from first-order to second-order at tricritical point

Results support the universality predicted by the Cardy-Jacobsen conjecture

Abstract

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out in the citizen supercomputer Ibercivis. Upon dilution, the pure model's first-order transition becomes of the second-order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their Random Field Ising Model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.