Entanglement percolation and spheres in $\mathbb{Z}^d$

DOI10.1214/22-EJP816zbMATH Open1507.60128arXiv2112.03538WikidataQ114060448 ScholiaQ114060448MaRDI QIDQ6384989

Publication date: 7 December 2021

Abstract: We obtain a new lower bound of 0.06576 for the 1-entanglement critical probability (in dimension 3), and prove that the critical point for the existence of a sphere surrounding the origin and intersecting only closed bonds in

m a t h b b Z^{d}

is greater than

f r a c 1 8 (d - 1)

,

d g e q 3

. This substantially improves the previous lower bounds and gives the correct order of magnitude for large

d

.

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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