Geodesic
Thermodynamics of the two-dimensional and three-dimensional Ising models in the static fluctuation approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 1, pp. 94-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the framework of an unified approximation called by the authors the static fluctuation approximation (SFA) coupled equations are derived for the magnetization and pair correlation functions. They can be applied for the Ising model of an arbitrary dimension with spins ($S=1/2$) located in the knots of an arbitrary lattice. The comparison with the available exact results shows the efficience, high precision and simplicity of the SFA. This makes it possible to describe the experiments on substances to which the Ising model can be applied. 
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R. R. Nigmatullin; V. A. Toboev. Thermodynamics of the two-dimensional and three-dimensional Ising models in the static fluctuation approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 1, pp. 94-106. http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a8/

[1] Montroll E., “Lektsii po modeli Izinga”, Ustoichivost i fazovye perekhody, Mir, M., 1973, 92–163 | MR

[2] Fedyanin V. K., Statisticheskaya fizika i kvantovaya teoriya polya, Nauka, M., 1973, 241–261 | MR

[3] Smart Dzh., Effektivnoe pole v teorii magnetizma, Mir, M., 1968

[4] Rudoi Yu. G., Statisticheskaya fizika i kvantovaya fizika, Nauka, M., 1973, 97–164

[5] Vilson K., Kogut Dzh., Renormalizatsionnaya gruppa i $\varepsilon$-razlozhenie, Mir, M., 1975

[6] Izyumov Yu. A., Kassan-ogly F. A., Skryabin Yu. N., Polevye metody v teorii ferromagnetizma, Nauka, M., 1974

[7] Gaunt O. S., Sykes M. F., J. Phys. A, 6:10 (1973), 1517–1526 | DOI | MR

[8] Frank B., Mitran O., J. Phys. C, C11:10 (1978), 2087–2101 | DOI

[9] Zhelifonov M. P., TMF, 8:3 (1971), 401–412

[10] Nigmatullin R. R., Toboev V. A., TMF, 68:1 (1986), 88–98 | MR

[11] Nigmatullin R. R., Physica, 116A (1982), 612–621 | DOI | MR

[12] Nigmatullin R. R., Toboev V. A., TMF, 74:1 (1988), 112–124

[13] Steiner M., Villian J., Windsor C., Adv. Phys., 25 (1976), 87–209 | DOI

[14] Kessel A. R., Berim G. O., Magnitnyi rezonans izingovskikh magnetikov, Nauka, M., 1982

[15] Nigmatullin R. R., Izv. vuzov. Fizika, 1981, no. 12, 18–20

[16] Morita T., Horiguchi T., J. Math. Phys., 12:6 (1971), 981–992 | DOI | MR

[17] Berim G. O., Kamalov R. G., TMF, 59:2 (1984), 297–306 | MR

[18] Baxter R. J., Enting I. G., J. Stat. Phys., 21:2 (1979), 103–123 | DOI | MR

[19] Abraham O. B., Phys. Lett., A43:2 (1973), 163–164 | DOI

[20] Bekster R., Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR

[21] Baker G. A., Phys. Rev. A, 136A:5 (1964), 1376–1380 | MR

[22] Mannari I., Kagejama H., Suppl. Progr. Theor. Phys., 1968, 269–279 | DOI | MR

[23] Patashinskii A. Z., Pokrovskii V. L., Fluktuatsionnaya teoriya fazovykh perekhodov, Nauka, M., 1975 | MR