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Related Experiment Video

Updated: May 24, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

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

Michael J Lee¹

¹Department of Physics and Astronomy, University of Canterbury, Christchurch, New Zealand.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 15, 2008

Summary

This study identifies a reliable pseudo-random number generator for high-precision simulations. It determines the percolation threshold for a 2D square lattice to be p_c = 0.59274598(4).

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Area of Science:

Computational physics
Statistical mechanics
Percolation theory

Background:

Percolation models describe the formation of connected clusters in random systems.
Accurate simulation of these models requires high-quality random number generation.
The two-dimensional square-lattice site percolation model is a fundamental system in statistical physics.

Purpose of the Study:

To identify a suitable pseudo-random number generator for high-precision Monte Carlo simulations.
To accurately determine the critical percolation threshold (p_c) for the 2D square-lattice site percolation model.

Main Methods:

Monte Carlo simulation techniques were employed.
Various pseudo-random number generators were tested for randomness.
An application-specific test was used to select the most appropriate generator for high-precision calculations.
Extensive computation and statistical analysis were performed.

Main Results:

A pseudo-random number generator suitable for high-precision calculations was identified.
The percolation threshold for the 2D square-lattice site percolation model was determined with high accuracy.
The obtained value is p_c = 0.59274598(4).

Conclusions:

The selected pseudo-random number generator is reliable for high-precision percolation studies.
The determined percolation threshold provides a benchmark value for this fundamental model.
This work contributes to the accurate computational study of phase transitions in disordered systems.