Vortex-line percolation in the three-dimensional complex |psi|^4 model

TL;DR

This study investigates the critical behavior of vortex-loop networks and magnetic properties in the 3D complex |psi|^4 model, revealing that different vortex connectivity definitions affect percolation thresholds and their relation to the phase transition.

Contribution

It provides a detailed analysis of vortex-loop percolation and its relation to phase transitions, highlighting the impact of connectivity definitions on critical behavior in the 3D complex |psi|^4 model.

Findings

Different vortex connectivity definitions yield distinct percolation thresholds.

Percolation thresholds do not match the thermodynamic phase transition point.

Vortex-loop networks exhibit varying critical behavior depending on connectivity criteria.

Abstract

In discussing the phase transition of the three-dimensional complex |psi|^4 theory, we study 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 investigate if both of them exhibit the same critical behavior leading to the same critical exponents and hence to a consistent description of the phase transition. Different percolation observables are taken into account and compared with each other. We find that different connectivity definitions for 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.