Plaquettes, Spheres, and Entanglement

2010/02/12 by Geoffrey R. Grimmett, Grimmett, Geoffrey R., Alexander E. Holroyd +1 · 2 citations
Mathematics · Physics and Astronomy · #60K35 #82B20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:60K35 #msc:82B20

paper · pdf · doi:10.48550/arxiv.1002.2623

arxiv created 2010/08/17 · arxiv updated 2010/08/18

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 >= μ^-2 where μis the connective constant for self-avoiding walks on Z³. Furthermore, when the edge density p is below this bound, the radius of the entanglement cluster containing the origin has an exponentially decaying tail.

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