Percolation in a three-dimensional non-symmetric multi-color loop model

TL;DR

This paper investigates the percolation transition in a three-dimensional non-symmetric multi-color loop model using Monte Carlo simulations, revealing critical exponents similar to the 3D XY model and analyzing the transition's relation to thermal criticality.

Contribution

The study provides the first detailed Monte Carlo analysis of a non-symmetric 3D loop model's percolation transition, including critical exponent estimation.

Findings

Percolation transition occurs near but not at the thermal critical temperature.

Correlation length exponent matches that of the 3D XY model within 6% error.

Finite-size analysis confirms the universality class of the transition.

Abstract

We conducted Monte Carlo simulations to analyze the percolation transition of a non-symmetric loop model on a regular three-dimensional lattice. We calculated the critical exponents for the percolation transition of this model. The percolation transition occurs at a temperature that is close to, but not exactly the thermal critical temperature. Our finite-size study on this model yielded a correlation length exponent that agrees with that of the three-dimensional XY model with an error margin of six per cent.