Plaquettes, Spheres, and Entanglement
Probability
2010-08-18 v2 Mathematical Physics
math.MP
Abstract
The high-density plaquette percolation model in d dimensions contains a surface that is homeomorphic to the (d-1)-sphere and encloses the origin. This is proved by a path-counting argument in a dual model. When d=3, this permits an improved lower bound on the critical point p_e of entanglement percolation, namely p_e >= \mu^-2 where \mu is the connective constant for self-avoiding walks on Z^3. Furthermore, when the edge density p is below this bound, the radius of the entanglement cluster containing the origin has an exponentially decaying tail.
Cite
@article{arxiv.1002.2623,
title = {Plaquettes, Spheres, and Entanglement},
author = {Geoffrey R. Grimmett and Alexander E. Holroyd},
journal= {arXiv preprint arXiv:1002.2623},
year = {2010}
}