Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation

TL;DR

This paper reviews and consolidates decades of research on 2D percolation, providing precise values for the percolation threshold, correction-to-scaling exponent, and susceptibility amplitude ratio, resolving previous uncertainties.

Contribution

It presents the most accurate and recent estimates of key percolation parameters in two dimensions, confirming and refining earlier values.

Findings

Percolation threshold p_c = 0.59274602(4)

Correction-to-scaling exponent Omega = 72/91 = 0.791

Susceptibility amplitude ratio C^+/C^- = 161.5(1.5)

Abstract

We summarize several decades of work in finding values for the percolation threshold p_c for site percolation on the square lattice, the universal correction-to-scaling exponent Omega, and the susceptibility amplitude ratio C^+/C^-, in two dimensions. Recent studies have yielded the precise values p_c = 0.59274602(4), Omega = 72/91 = 0.791, and C^+/C^- = 161.5(1.5), resolving long-standing controversies about the last two quantities and verifying the widely used value p_c = 0.592746 for the first.