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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)