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 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, suggesting that they are exact. They also agree with exponents for hulls proposed recently by Aharony and Asikainen, based upon results of den Nijs. A corrections scaling form evidently applicable to site percolation is also found.