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Critical p=1/2 in percolation on semi-infinite strips
1Faculty of Physics and Astronomy, University of Wrocław, 50-204 Wrocław, Poland.
Physical Review. E
|November 28, 2019
Summary
Site percolation on lattices in semi-infinite strips shows a universal probability of 1/2 for clusters touching three sides at the percolation threshold. This finding applies to planar and self-matching lattices, revealing asymptotic symmetry. Keywords: site percolation, lattice, probability, universality.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- Percolation theory studies the formation of connected clusters in random systems.
- Understanding boundary effects is crucial for lattice models.
Purpose of the Study:
- Investigate site percolation on lattices confined to a semi-infinite strip.
- Determine the probability of cluster contact with system boundaries at the percolation threshold.
Main Methods:
- Analysis of site percolation on triangular and square lattices.
- Examination of cluster connectivity in a semi-infinite strip geometry.
- Theoretical arguments for universality and asymptotic symmetry.
Main Results:
- The probability of a cluster touching three sides of the strip at the percolation threshold converges to 1/2.
- This 1/2 limit is proposed as a universal value for planar systems.
- The result is expected to hold for finite systems on self-matching lattices.
Conclusions:
- A universal probability of 1/2 governs cluster boundary contact in confined percolation systems.
- Asymptotic symmetry of separation lines underlies this universal behavior.
- The findings offer insights into critical phenomena in reduced dimensions.
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