O(2) symmetry breaking vs. vortex loop percolation

TL;DR

This paper investigates how different geometric definitions of vortex loops in a 3D O(2) symmetric system relate to phase transitions, revealing that percolation does not necessarily align with thermodynamic criticality.

Contribution

It demonstrates that the percolation transition of vortex loops depends on the definition used and does not always match the thermodynamic phase transition, challenging assumptions about universality.

Findings

Percolation transition varies with vortex network definition.

Percolation does not coincide with thermodynamic transition.

Geometric percolation observables lack universal critical behavior.

Abstract

We study with lattice Monte Carlo simulations the relation of global O(2) symmetry breaking in three dimensions to the properties of a geometrically defined vortex loop network. We find that different definitions of constructing a network lead to different results even in the thermodynamic limit, and that with typical definitions the percolation transition does not coincide with the thermodynamic phase transition. These results show that geometrically defined percolation observables need not display universal properties related to the critical behaviour of the system, and do not in general survive in the field theory limit.