Geodesic
Ising model with nonmagnetic dilution on recursive lattices
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 304-311

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Using a method for composing self-consistent equations, we construct a class of approximate solutions of the Ising problem that are a generalization of the Bethe approximation. We show that some of the approximations in this class can be interpreted as exact solutions of the Ising model on recursive lattices. For these recursive lattices, we find exact values of the thresholds of percolation through sites and couplings and show that for the Ising model of a diluted magnet, our method leads to exact values for these thresholds.
Keywords: Ising model, crystal lattice, magnet with nonmagnetic dilution, recursive lattice. 
@article{TMF_2020_202_2_a8,
     author = {S. V. Semkin and V. P. Smagin and E. G. Gusev},
     title = {Ising model with nonmagnetic dilution on recursive lattices},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {304--311},
     publisher = {mathdoc},
     volume = {202},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a8/}
}
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S. V. Semkin; V. P. Smagin; E. G. Gusev. Ising model with nonmagnetic dilution on recursive lattices. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 304-311. http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a8/