Geodesic
On the critical indices in three-dimensional percolation in the problems of lattice points and solid spheres
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2010), pp. 67-80

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Three-dimensional lattice points problems for simple cubic lattice and solid spheres in chaotic motion are considered. Additional (to two-exponential scaling) relations between indices are indicated: $2-\alpha-\gamma=\nu$ (or $\nu d-\gamma=\nu$) and $\beta=-2\alpha$. Numerical values of three-dimensional critical indices are defined: $\alpha=-2/11$, $\eta=0,$ $\beta=4/11$, $\nu=8/11$, $\gamma=16/11$ and $\delta=5$.
Keywords: percolation, critical exponent, lattice, solid sphere. 
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     author = {S. R. Gallyamov and S. A. Mel'chukov},
     title = {On the critical indices in three-dimensional percolation in the problems of lattice points and solid spheres},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {67--80},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_2_a5/}
}
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S. R. Gallyamov; S. A. Mel'chukov. On the critical indices in three-dimensional percolation in the problems of lattice points and solid spheres. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2010), pp. 67-80. http://geodesic.mathdoc.fr/item/VUU_2010_2_a5/