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

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.

References in corpus (4)

• 2D growth processes: SLE and Loewner chains
• Correction-to-scaling exponent for two-dimensional percolation
• Numerical results for crossing, spanning and wrapping in two-dimensional percolation
• The density of critical percolation clusters touching the boundaries of strips and squares

Cited by in corpus (5)

• Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit
• Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions
• Bond percolation on simple cubic lattices with extended neighborhoods
• Precise bond percolation thresholds on several four-dimensional lattices
• Jammed systems of oriented dimers always percolate on hypercubic lattices