Phases of the three-state Potts model in three spatial dimensions

TL;DR

This study numerically explores the three-state Potts model in three dimensions, revealing cluster behaviors and interactions near the first-order phase transition, and explaining the transition's weakness.

Contribution

It provides detailed numerical analysis of cluster structures and interactions in the 3D three-state Potts model near the phase transition.

Findings

Clusters of like spins have irregular boundaries.

Non-favored spins attract each other with finite range.

First-order transitions are weak due to domain interactions.

Abstract

The three-state Potts model is numerically investigated on three-dimensional simple cubic lattices of up to \(128^3\) volume, concentrating on the neighborhood of the first-order phase transition separating the ordered and disordered phases. In both phases clusters of like spins are observed with irregular boundaries. In the ordered phase the two different non-favored spins are found to attract each other with a long but finite range. As a result, the neighborhoods of the non-favored spins are interpreted as domains of the disordered phase. This explains why the first-order phase transitions associated with the global \(Z_3\) symmetry, including the SU(3) pure-gauge one, are so weak.