### Abstract

We show that the distribution of the percolation threshold in a large finite system does not converge to a Gaussian when the size of the system goes to infinity, provided that the two widely accepted definitions of correlation length are equivalent. The shape of the distribution is thus directly related to the presence or absence of logarithmic corrections in the power law for the correlation length. The result is obtained by estimating the rate of decay of tail of the limiting distribution in terms of the correlation length exponent v. All results are rigorously proven in the 2D case. Generalizations for three dimensions are also discussed.

Original language | English (US) |
---|---|

Article number | 013 |

Pages (from-to) | 7127-7133 |

Number of pages | 7 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 28 |

Issue number | 24 |

DOIs | |

State | Published - 1995 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*28*(24), 7127-7133. [013]. https://doi.org/10.1088/0305-4470/28/24/013

}

*Journal of Physics A: Mathematical and General*, vol. 28, no. 24, 013, pp. 7127-7133. https://doi.org/10.1088/0305-4470/28/24/013

**The probability distribution of the percolation threshold in a large system.** / Berlyand, Leonid V.; Wehr, J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The probability distribution of the percolation threshold in a large system

AU - Berlyand, Leonid V.

AU - Wehr, J.

PY - 1995

Y1 - 1995

N2 - We show that the distribution of the percolation threshold in a large finite system does not converge to a Gaussian when the size of the system goes to infinity, provided that the two widely accepted definitions of correlation length are equivalent. The shape of the distribution is thus directly related to the presence or absence of logarithmic corrections in the power law for the correlation length. The result is obtained by estimating the rate of decay of tail of the limiting distribution in terms of the correlation length exponent v. All results are rigorously proven in the 2D case. Generalizations for three dimensions are also discussed.

AB - We show that the distribution of the percolation threshold in a large finite system does not converge to a Gaussian when the size of the system goes to infinity, provided that the two widely accepted definitions of correlation length are equivalent. The shape of the distribution is thus directly related to the presence or absence of logarithmic corrections in the power law for the correlation length. The result is obtained by estimating the rate of decay of tail of the limiting distribution in terms of the correlation length exponent v. All results are rigorously proven in the 2D case. Generalizations for three dimensions are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0004592957&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004592957&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/28/24/013

DO - 10.1088/0305-4470/28/24/013

M3 - Article

AN - SCOPUS:0004592957

VL - 28

SP - 7127

EP - 7133

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 24

M1 - 013

ER -