Conducting-angle-based percolation in the XY model

TL;DR

This paper introduces a percolation model based on the XY spin configurations, revealing that the percolation transition aligns with standard 2D percolation universality, regardless of the XY model's temperature phase.

Contribution

It defines a novel percolation problem on the XY model and demonstrates its critical behavior matches classical percolation theory through Monte Carlo simulations.

Findings

Percolation transitions occur at specific conducting angles.

Critical exponents match the 2D percolation universality class.

The model's critical behavior is consistent across temperature phases.

Abstract

We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting angle. The percolation properties of this model are studied by means of Monte Carlo simulations and a finite-size scaling analysis. Our simulations show the existence of percolation transitions when the conducting angle is varied, and we determine the transition point for several values of the XY coupling. It appears that the critical behavior of this percolation model can be well described by the standard percolation theory. The critical exponents of the percolation transitions, as determined by finite-size scaling, agree with the universality class of the two-dimensional percolation model on a uniform substrate. This holds over the whole temperature range, even in the low-temperature phase where the XY substrate is critical in the sense that it displays algebraic decay of correlations.