Quasi Long Range Order and Vortex Lattice in the Three State Potts Model

TL;DR

This paper investigates the phase transitions in the three-state Potts model, revealing how vortex and domain wall dynamics lead to distinct intermediate phases with unique symmetries and order properties.

Contribution

It demonstrates how vortex core energy influences the nature of phase transitions and the emergence of quasi long-range order and vortex lattices in the model.

Findings

Decoupling of vortex and domain wall proliferation creates an intermediate phase with U(1) symmetry.

Lower vortex core energy results in a vortex lattice phase.

Vortex dynamics critically determine the phase transition structure.

Abstract

We show that the order-disorder phase transition in the three state Potts ferromagnet on a square lattice is driven by a coupled proliferation of vortices and domain walls. Raising the vortex core energy above a certain value decouples the proliferation and splits the transition into two. The phase between the two transitions exhibits an emergent U(1) symmetry and quasi long range order. Lowering the core energy also splits the order-disorder transition but the proliferation does not decouple and a vortex lattice appears as the intermediate phase.