Pseudorandom Number Generators and the Square Site Percolation Threshold

TL;DR

This paper evaluates various pseudorandom number generators in a Monte Carlo simulation of 2D square site percolation, identifying a high-precision generator and estimating the percolation threshold with improved accuracy.

Contribution

It introduces a test for selecting suitable pseudorandom generators for percolation simulations and provides a precise estimate of the percolation threshold.

Findings

Identified a pseudorandom generator suitable for high-precision calculations.

Estimated the percolation threshold as pc = 0.59274598(4).

Validated the reliability of the simulation results.

Abstract

A select collection of pseudorandom number generators is applied to a Monte Carlo study of the two dimensional square 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 pc = 0.59274598(4) is obtained for the percolation threshold.