Simultaneous analysis of three-dimensional percolation models

Abstract

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, 2013, 87(5): 052107], it is observed that in comparison with dimensionless ratios based on cluster-size distribution, certain wrapping probabilities exhibit weaker finite-size corrections and are more sensitive to the deviation from percolation threshold p_c, and thus provide a powerful means for determining p_c. We analyze the numerical data of the wrapping probabilities simultaneously such that universal parameters are shared by the aforementioned models, and thus significantly improved estimates of p_c are obtained.

Graphical abstract

Keywords

percolation models / Monto Carlo simulation / simultaneous fit