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The problem of approximating the average number of cluster sites on square percolation lattices is studied. For uniformly weighted lattices of finite size, a model is proposed based on a generalization of the logistic function that describes the transition between two slant asymptotes. To obtain statistical estimates of the model coefficients, the nonlinear least squares method is used, which made it possible to obtain preliminary estimates of the percolation threshold error for various sizes of the percolation lattice.
Moskalev P. V., Onishchenko L. S. 2023. Statistical estimation of the average number of cluster sites on uniformly weighted square lattices. PREPRINTS.RU. https://doi.org/10.24108/preprints-3112911