Unexpected results of the phase transitions of four-state Potts model on the square and the honeycomb lattices

TL;DR

This study challenges the common belief by showing persistent first-order transition features in the four-state Potts model on square lattices and early signs of second-order transitions on honeycomb lattices, based on extensive simulations.

Contribution

The paper provides extensive simulation evidence that contradicts previous assumptions about phase transition types in the four-state Potts model on different lattices.

Findings

First-order transition features persist on the square lattice.

Second-order transition characteristics appear on small honeycomb lattices.

Pseudo-first-order transitions were not observed in the simulations.

Abstract

It is widely believed that the phase transition for the four-state ferromagnetic Potts model on the square lattice is of the pseudo-first order. Specifically, it is expected that first-order phase transition behavior is found on small lattices and that the true nature of second-order phase transition only emerges with large system sizes. It is also intuitively expected that for other geometries, the types of the associated phase transitions should be identical to that of the square lattice. However, after simulating more than 16 million spins for the four-state Pott model, we observe that a feature of first-order phase transition persists on the square lattice. Additionally, a characteristic of second-order phase transition already appears on a small honeycomb lattice. Indications of a pseudo-first-order phase transition were not found in our investigation. This suggests that a thorough analytic calculation may be required to develop a better understanding of the presented results.