Uniqueness of the critical probability for percolation in the two dimensional Sierpinski carpet lattice
Yasunari Higuchi, Xian-Yuan Wu
TL;DR
This paper proves that the critical probability for percolation on the two-dimensional Sierpinski carpet lattice is unique and the phase transition is sharp, extending previous results to this fractal structure.
Contribution
It establishes the uniqueness of the critical probability and sharpness of the transition specifically for the Sierpinski carpet lattice, extending Kumagai's results.
Findings
Critical probability for the Sierpinski carpet lattice is unique.
The phase transition in this lattice is sharp.
The results extend previous work to a fractal lattice.
Abstract
We prove that the critical probability for the Sierpinski carpet lattice in two dimensions is uniquely determined. The transition is sharp. This extends the Kumagai's result to the original Sierpinski carpet lattice.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Markov Chains and Monte Carlo Methods