Partial Breaking of Three-Fold Symmetry via Percolation of a Domain Wall

TL;DR

This paper investigates how suppressing vortex strings affects phase transitions in the three-state Potts model on different lattices, revealing distinct intermediate phases with partial symmetry breaking and long-range order.

Contribution

It demonstrates that vortex suppression leads to different intermediate phases on cubic and square lattices, linked to domain wall percolation patterns.

Findings

Suppression of vortices on cubic lattice causes partial three-fold symmetry breaking.

On square lattice, vortex suppression results in an intermediate phase with U(1) symmetry.

Domain wall percolation behavior explains the differences between phases.

Abstract

We show that suppression of vortex strings splits the order-disorder transition in the three-state Potts ferromagnet on a simple cubic lattice and opens up an intermediate phase characterized by partial breaking of the three-fold symmetry and long-range order. In contrast, suppression of vortices in the same model on a square lattice results in an intermediate phase with enhanced U(1) symmetry and quasi-long-range order. We show that the difference between the two phases originates from distinct patterns of domain wall proliferation. A domain wall, separating the two most populous spin states, percolates on its own in the former phase but remains at a percolation threshold in the latter.