Correction-to-scaling exponent for two-dimensional percolation

TL;DR

This paper derives bounds on correction-to-scaling exponents in 2D percolation using Cardy's crossing probability, supporting the conjecture that these bounds are exact and providing a scaling form for site percolation.

Contribution

It establishes upper bounds on correction-to-scaling exponents in 2D percolation based on Cardy's results, suggesting these bounds are exact.

Findings

Bounds on correction-to-scaling exponents are consistent with previous measurements.

New measurements for bond percolation support the bounds.

A universal scaling form for site percolation is identified.

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.