Geodesic
On nonscaling probability function for passing in a~simple cubic lattice: theory and computer experiment
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2009), pp. 29-36

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Using known properties of the probability function for passing in a simple cubic lattice with $L=2$ in approximation of a linear relation between a passing threshold of an infinite lattice $x_c$ and average value $x_{cL}$ of a finite lattice, we introduce a nonscaling probability function of passing of a lattice with $L>2$. We show that on the passing threshold nonscaling probabilities for all simple cubic lattices are the same. Computer experiments based on the Monte-Carlo method are in agreement with the theory proposed.
Keywords: percolation, lattice, passing probability, nonscaling, computer experiment. 
@article{VUU_2009_2_a3,
     author = {S. R. Gallyamov and S. A. Mel'chukov},
     title = {On nonscaling probability function for passing in a~simple cubic lattice: theory and computer experiment},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {29--36},
     publisher = {mathdoc},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2009_2_a3/}
}
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S. R. Gallyamov; S. A. Mel'chukov. On nonscaling probability function for passing in a~simple cubic lattice: theory and computer experiment. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2009), pp. 29-36. http://geodesic.mathdoc.fr/item/VUU_2009_2_a3/