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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Ziman J. M., Models of disorder, Cambridge University Press, N.Y., London, Melbourne, 1979 | MR

[2] Efros A. L., Fizika i geometriya besporyadka, Bibliotechka “Kvant”, 19, Nauka, M., 1982, 176 pp. | MR

[3] Shklovskii B. I., Efros A. L., Elektronnye svoistva legirovannykh poluprovodnikov, Nauka, M., 1979

[4] Tarasevich Yu. Yu., Perkolyatsiya: teoriya, prilozheniya, algoritmy, Editorial URSS, M., 2002, 112 pp.

[5] Gallyamov S. R., “Porog protekaniya prostoi kubicheskoi reshetki v zadache uzlov v modeli reshetki Bete”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2008, no. 3, 109–115

[6] Levinshtein M. E., Shur M. S., Shklovskii B. I., Efros A. L., “O svyazi mezhdu kriticheskimi indeksami teorii protekaniya”, ZhETF, 69 (1975), 386 | MR

[7] Lorenz C. D., Ziff R. M., “Universality of the excess number of clasters and the crossing probability function in three-dimensional percolation”, J. Phys. A: Math. Gen., 31 (1998), 8147–8157 | DOI | Zbl

[8] Venttsel E. S., Ovcharov L. A., Zadachi i uprazhneniya po teorii veroyatnostei, Vyssh. shk., M., 2006, 123 pp.

[9] Kadanoff L. P. et al., “Static Phenomena Near Critical Points: Theory and Experiment”, Rev. Mod. Phys., 39 (1967), 395–431 | DOI

[10] Wilson K. G., “Renormalization group and critical phenomena. 1. Renormalization group and Kadanoff scaling picture”, Phys. Rev. B, 4 (1971), 3174 | DOI | Zbl