Exact Percolation Probability on the Square Lattice

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.

23 pages, 14 figures, 5 tables

References in corpus (4)

• The ground state energy at unitarity
• Complementary algorithms for graphs and percolation
• Bond percolation thresholds on Archimedean lattices from critical polynomial roots
• Percolation is Odd

Cited by in corpus (3)

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