Pseudo-random-number generators and the square site percolation threshold

2008/07/10 by Michael J. Lee · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Chaos-based Image/Signal Encryption #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn

paper · pdf · doi:10.1103/physreve.78.031131

11 pages, 6 figures

arxiv created 2008/07/10 · openalex publication_date 2008/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Selected pseudo-random-number generators are applied to a Monte Carlo study of the two-dimensional square-lattice site percolation model. A generator suitable for high precision calculations is identified from an application specific test of randomness. After extended computation and analysis, an ostensibly reliable value of p_c=0.59274598(4) is obtained for the percolation threshold.

Citations

• TestU01
• Improved long-period generators based on linear recurrences modulo 2
• A fast Monte Carlo algorithm for site or bond percolation
• Four-tap shift-register-sequence random-number generators
• Percolation

Cited by

• Percolation in networks with voids and bottlenecks
• Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions
• A new scale-invariant ratio and finite-size scaling for the stochastic susceptible–infected–recovered model
• Factorization of percolation density correlation functions for clusters touching the sides of a rectangle

Related

• Random site percolation thresholds on square lattice for complex neighborhoods containing sites up to the sixth coordination zone
• A fast Monte Carlo algorithm for site or bond percolation
• Site percolation on planarΦ3random graphs
• Square-lattice site percolation at increasing ranges of neighbor bonds
• Incipient Spanning Clusters in Square and Cubic Percolation