Topological percolation on a square lattice

S. K. Nechaev, O. A. Vasilyev

Published 2004-01-04, updated 2004-01-11Version 2

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.