Percolation on two- and three-dimensional lattices

TL;DR

This paper applies an efficient Monte Carlo algorithm to study percolation on various 2D and 3D lattices, providing accurate estimates of critical parameters and confirming universality of wrapping probabilities.

Contribution

It demonstrates the effectiveness of a recent Monte Carlo method for analyzing percolation, yielding precise critical data across multiple lattice types.

Findings

Accurate critical thresholds for different lattices

Confirmation of universality in wrapping probabilities

Efficient analysis with small system sizes

Abstract

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent and critical concentration are obtained for the square, simple cubic, HCP and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.