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 (13)

• Critical Percolation in Finite Geometries
• Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation
• On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice
• Four-tap shift-register-sequence random-number generators
• Exact bond percolation thresholds in two dimensions
• Shape-dependent universality in percolation
• Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems
• Simulation of percolation on massively-parallel computers
• Fractal geometry of critical Potts clusters
• The O(n) model on the annulus
• Effects of boundary conditions on the critical spanning probability
• Numerical results for crossing, spanning and wrapping in two-dimensional percolation
• Conducting-angle-based percolation in the XY model

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