Corrections to finite size scaling in percolation

  title={Corrections to finite size scaling in percolation},
  author={Paulo Murilo C. de Oliveira and Rafael A. N{\'o}brega and Dietrich Stauffer},
  journal={Brazilian Journal of Physics},
A 1 = L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18; 22;... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at pc for an annulus with aspect ratio r = 1=2 is estimated as… 

Figures and Tables from this paper

From discrete to continuous percolation in dimensions 3 to 7

The convergence of a discrete model to its continuous limit is controlled by a power-law dependency with a universal exponent θ=3/2, which allows us to estimate the continuous percolation thresholds in a model of aligned hypercubes in dimensions d=3,…,7 with accuracy far better than that attained using any other method before.

Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length k (k-mers) on two-dimensional square lattices. The

Are the tails of percolation thresholds Gaussians

Evidence is shown on square lattices that the probability distribution of percolation thresholds in finite lattices is numerically not yet answered at all, based on a further improvement of the Monte Carlo data.

Percolation of aligned rigid rods on two-dimensional square lattices.

The results show that the percolation threshold exhibits a decreasing function when it is plotted as a function of the kmer size, and in the case of aligned kmers, the intersection points of the curves of R(L,k)(p) for different system sizes exhibit nonuniversal critical behavior, varying continuously with changes in the kmers size.

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.



Numerical recipes in C

The Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08.


  • Rev. E64, 016706 (2001); Phys. Rev. Lett. 85, 4104
  • 2000

J. Phys. A16

  • J. Phys. A16
  • 1980

Phys. Rev. E66

  • Phys. Rev. E66
  • 2002


  • Phys. 577 (1980); N. Jan, T. Lookman and D. Stauffer, J. Phys. A16, L117 (1983); P.M.C. de Oliveira, S. Moss de Oliveira and S.L.A. de Queiroz, Physica A175, 345
  • 1991

J. Stat. Phys

  • J. Stat. Phys
  • 1994

Int. J. Mod. Phys. C11

  • Int. J. Mod. Phys. C11
  • 1999


  • Rev. E66, 016129
  • 2002


  • 75, 1167
  • 1994


  • Rev. E53, 235
  • 1996