Vortex-Line Percolation in the Three-Dimensional Complex Ginzburg-Landau Model

TL;DR

This study investigates the vortex-loop network and magnetic properties in the 3D complex Ginzburg-Landau model near criticality, revealing that different vortex definitions lead to varying percolation thresholds that do not match the phase transition point.

Contribution

It provides a high-precision Monte Carlo analysis of vortex-loop percolation and highlights discrepancies between geometrical and thermodynamic critical behaviors.

Findings

Different vortex definitions yield distinct percolation thresholds.

Percolation thresholds do not coincide with the thermodynamic phase transition.

Vortex-loop networks exhibit non-universal critical behavior.

Abstract

We study the phase transition of the three-dimensional complex |psi|^4 theory by considering the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using high-precision Monte Carlo techniques we examine an alternative formulation of the geometrical excitations in relation to the global O(2)-symmetry breaking, and check if both of them exhibit the same critical behavior leading to the same critical exponents and therefore to a consistent description of the phase transition. Different percolation observables are taken into account and compared with each other. We find that different definitions of constructing the vortex-loop network lead to different results in the thermodynamic limit, and the percolation thresholds do not coincide with the thermodynamic phase transition point.