Two-Dimensional Critical Potts and its Tricritical Shadow

TL;DR

This paper explores how geometrical objects like spin clusters in the 2D Potts model encode critical and tricritical behaviors, linking fractal structures to phase transitions such as superfluidity and Bose-Einstein condensation.

Contribution

It introduces a geometrical perspective on critical phenomena in the 2D Potts model, distinguishing between standard and tricritical behaviors through cluster types.

Findings

Fortuin-Kasteleyn clusters encode critical behavior

Geometrical clusters describe tricritical behavior

Application to superfluid and Bose-Einstein phase transitions

Abstract

These notes give examples of how suitably defined geometrical objects encode in their fractal structure thermal critical behavior. The emphasis is on the two-dimensional Potts model for which two types of spin clusters can be defined. Whereas the Fortuin-Kasteleyn clusters describe the standard critical behavior, the geometrical clusters describe the tricritical behavior that arises when including vacant sites in the pure Potts model. Other phase transitions that allow for a geometrical description discussed in these notes include the superfluid phase transition and Bose-Einstein condensation.