Corrections to Finite Size Scaling in Percolation

TL;DR

This paper introduces a 1/L-expansion method for finite size scaling in percolation, using Monte Carlo simulations on various lattice sizes to estimate critical thresholds and universal spanning probabilities.

Contribution

It proposes a new 1/L-expansion approach for finite size scaling in percolation and applies it to estimate critical thresholds and universal probabilities.

Findings

Estimated critical threshold pc for the lattice.

Determined universal spanning probability C at pc.

Validated the 1/L-expansion method with simulation data.

Abstract

A 1/L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at pc for an annulus with aspect ratio r=1/2 is estimated as C = 0.876657(45).