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Condensed Matter > Statistical Mechanics

arXiv:1906.10543 (cond-mat)
[Submitted on 24 Jun 2019 (v1), last revised 22 Jul 2019 (this version, v2)]

Title:Critical p=1/2 in percolation on semi-infinite strips

Authors:Zbigniew Koza
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Abstract:We study site percolation on lattices confined to a semi-infinite strip. For triangular and square lattices we find that the probability that a cluster touches the three sides of such a system at the percolation threshold has the continuous limit 1/2 and argue that this limit is universal for planar systems. This value is also expected to hold for finite systems for any self-matching lattice. We attribute this result to the asymptotic symmetry of the separation lines between alternating spanning clusters of occupied and unoccupied sites formed on the original and matching lattice, respectively.
Subjects: Statistical Mechanics (cond-mat.stat-mech)
Cite as: arXiv:1906.10543 [cond-mat.stat-mech]
  (or arXiv:1906.10543v2 [cond-mat.stat-mech] for this version)
  https://doi.org/10.48550/arXiv.1906.10543
Journal reference: Phys. Rev. E 100, 042115 (2019)
Related DOI: https://doi.org/10.1103/PhysRevE.100.042115

Submission history

From: Zbigniew Koza [view email]
[v1] Mon, 24 Jun 2019 13:30:56 UTC (71 KB)
[v2] Mon, 22 Jul 2019 06:51:07 UTC (72 KB)
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