Correction-to-scaling exponent for two-dimensional percolation

Abstract

We show that the correction-to-scaling exponents in two-dimensional percolation are bounded by Omega <= 72/91, omega = D Omega <= 3/2, and Delta_1 = nu omega <= 2, based upon Cardy's result for the critical crossing probability on an annulus. The upper bounds are consistent with many previous measurements of site percolation on square and triangular lattices, and new measurements for bond percolation presented here, suggesting this result is exact. A scaling form evidently applicable to site percolation is also found.

References in corpus (5)

• On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice
• Exact bond percolation thresholds in two dimensions
• Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems
• The O(n) model on the annulus
• Numerical results for crossing, spanning and wrapping in two-dimensional percolation