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

  title={Pseudo-random-number generators and the square site percolation threshold.},
  author={Michael J. Lee},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={78 3 Pt 1},
  • Michael J. Lee
  • Published 10 July 2008
  • Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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. 

Figures and Tables from this paper

Site percolation simulation and percolation threshold

This paper will briefly introduce the theory of site percolation. Meanwhile, the study of the percolation threshold is also introduced. Firstly, the basic model is implemented in Java. Assume that

Estimates of threshold and strength of percolation clusters on square lattices with (1,d)-neighborhood

A new method of averaging the relative frequencies of the target subset of lattice sites is proposed, based on the SPSL package, released under GNU GPL-3 using the free programming language R.

Percolation in a triangle on a square lattice

Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice and spanning the

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible–infected–recovered model

The critical behavior of the stochastic susceptible–infected–recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the

Critical behavior of the susceptible-infected-recovered model on a square lattice.

  • T. ToméR. Ziff
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
The critical behavior of the stochastic asynchronous susceptible-infected-recovered model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamicPercolation cluster growth, as is demonstrated explicitly.

Site trimer percolation on square lattices.

Percolation of site trimers (k-mers with k=3) is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem to establish the tendency of p(c) to decrease as k increases.

Postprocessing techniques for gradient percolation predictions on the square lattice.

This work concludes that, due to skewness in the distribution of occupation probabilities visited the average does not converge monotonically to the true percolation threshold, and identifies several alternative metrics which do exhibit monotonic convergence and document their observed convergence rates.



Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in

Applications of percolation theory

Connectivity as the Essential Physics of Disordered Systems Elements of Percolation Theory Characterization of Porous Media Earthquakes, and Fracture and Fault in Patterns in Heterogeneous Rock

Applications of number theory to numerical analysis

1. Algebraic Number Fields and Rational Approximation.- 1.1. The units of algebraic number fields.- 1.2. The simultaneous Biophantine approximation of an integral basis.- 1.3. The real eyelotomie

The Art in Computer Programming

Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.


Random Struct

  • Algorithms 26, 392
  • 2005

Laboratory for Scientific Computing

  • University of Michigan, Report No. 88-4, Footnote 26
  • 1988

ANZIAM Journal 48

  • C188
  • 2007