Monte Carlo and series study of corrections to scaling in two-dimensional percolation

Abstract

Corrections to scaling for percolation cluster numbers in two dimensions are studied by Monte Carlo simulations of very large systems (up to 17*10⁹ lattice sites) and by series analysis. Both series and Monte Carlo work suggests that the value of the correction-to-scaling exponent is slightly lower at the percolation threshold than away from it. Moreover, the corrections to scaling observed at p_c ( Omega equivalent to 0.64) might be due to the mixing of scaling fields rather than to the irrelevant scaling fields. The Monte Carlo results are compatible with finite-size scaling, and finite-size scaling corrections are estimated. Technical problems associated with Monte Carlo simulation of very large systems are discussed in an appendix.