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arXiv · 2109.12102

Exact Percolation Probability on the Square Lattice

Stephan Mertens
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Abstract

We present an algorithm to compute the exact probability $R_{n}(p)$ for a site percolation cluster to span an $n\times n$ square lattice at occupancy $p$. The algorithm has time and space complexity $O(\lambda^n)$ with $\lambda \approx 2.6$. It allows us to compute $R_{n}(p)$ up to $n=24$. We use the data to compute estimates for the percolation threshold $p_c$ that are several orders of magnitude more precise than estimates based on Monte-Carlo simulations.

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Stephan Mertens. 2021-09-24. Exact Percolation Probability on the Square Lattice. https://doi.org/10.1088/1751-8121%2Fac4195

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