A simple algorithm to test for linking to Wilson loops in percolation

TL;DR

This paper introduces a straightforward algorithm to determine if loops in percolation clusters link a fixed reference loop, applicable in 2D and 3D, with results aligning with theoretical predictions.

Contribution

A simple burning algorithm is proposed to efficiently test linking of loops in percolation clusters, advancing methods in gauge theory contexts.

Findings

Algorithm successfully tests linking at criticality in 2D and 3D

Results agree with theoretical predictions in 2D

Provides a practical tool for gauge theory studies

Abstract

A simple burning or epidemic type of algorithm is developed in order to test whether any loops in percolation clusters link a fixed reference loop, a problem considered recently by Gliozzi, Lottini, Panero, and Rago in the context of gauge theory. We test our algorithm at criticality in both 2d, where the behavior agrees with a theoretical prediction, and in 3d.