Topological percolation on a square lattice

TL;DR

This paper studies topological percolation on a square lattice, showing it belongs to the 2D bond percolation universality class, and provides analytical and numerical results for the critical threshold and exponents.

Contribution

It introduces the concept of topological percolation in a (2+1)-dimensional system and establishes its universality class, along with analytical and numerical characterization.

Findings

Topological percolation belongs to the 2D bond percolation universality class.

Critical exponents and thresholds for topological phase transition are computed.

Numerical results confirm analytical predictions.

Abstract

We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the topological percolation threshold and the critical exponents of topological phase transition. Our numerical check confirms well obtained analytical results.