Re-examination of seven-dimensional site percolation thresholds

TL;DR

This paper re-examines seven-dimensional site percolation thresholds using Monte Carlo simulations and series estimates, providing insights into corrections to scaling and supporting renormalization group predictions.

Contribution

It offers a refined estimate of the seven-dimensional site percolation threshold and clarifies the nature of corrections to scaling above the upper critical dimension.

Findings

Monte Carlo simulations support series estimates for p_c

Corrections to scaling align with renormalization group predictions

Simple 1/L extrapolation is less favored for high dimensions

Abstract

Monte Carlo simulations alone could not clarify the corrections to scaling for the size-dependent p_c(L) above the upper critical dimension. Including the previous series estimate for the bulk threshold $p_c(\infty)$ gives preference for the complicated corrections predicted by renormalization group and against the simple 1/L extrapolation. Additional Monte-Carlo simulations using the Leath method corroborate the series result for p_c.