Geodesic
Generalized hierarchical model of a scalar ferromagnet in the method of collective variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 2, pp. 268-277 Cet article a éte moissonné depuis la source Math-Net.Ru

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By means of the method of collective variables and certain approximations a hierarchical representation is obtained for the partition function of the ferromagnetic Ising model with both short- and long-range interactions. It is shown that in the latter case the representation is, apart from a factor, identical to the exact representation of the partition function of the Dys0n model obtained by the same method. The approximations that lead from the Ising model to the Dyson model are analyzed. 
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     title = {Generalized hierarchical model of a scalar ferromagnet in the method of collective variables},
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Yu. V. Kozitskii; I. R. Yukhnovskii. Generalized hierarchical model of a scalar ferromagnet in the method of collective variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 51 (1982) no. 2, pp. 268-277. http://geodesic.mathdoc.fr/item/TMF_1982_51_2_a12/

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

[2] Kadanoff L. P., Physics (New York), 2:6 (1966), 263–273

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

[4] Dyson F. J., Commun. Math. Phys., 12 (1969), 91–107 | DOI | MR | Zbl

[5] Bleher P. M., Sinai Ya. G., Commun. Math. Phys., 33 (1973), 23–42 ; 45 (1975), 247–278 ; Блехер П. М., Синай Я. Г., ЖЭТФ, 67:1(7) (1974), 391–396 | DOI | MR | DOI | MR

[6] Blekher P. M., Tr. MMO, 33 (1975), 155–222 ; УМН, 32:6(198) (1977), 243–244 | MR

[7] Kim D., Thompson C. J., J. Phys. A: Math. Gen., 10:9 (1977), 1579–1598 | DOI | MR

[8] Baker G. A., Jr., Golner A., Phys. Rev., B16:5 (1977), 2081–2094 | DOI

[9] Yukhnovskii I. R., Rudavskii Yu. K., Primenenie metoda kollektivnykh peremennykh k issledovaniyu modeli Izinga. I: Statisticheskaya summa, Preprint ITF-74-171R, ITF AN USSR, Kiev, 1974; Применение метода коллективных переменных к модели Изинга. II: Исследование поведения парной корреляционной функции в окрестности точки фазового перехода, Препринт ИТФ-75-13Р, ИТФ АН УССР, Киев, 1975; УФЖ, 22:1 (1977), 50–59 | MR

[10] Yukhnovskii I. R., UFZh, 22:2 (1977), 328–338 ; 4, 484–493; ДАН СССР, 232:2 (1977), 312–315 | MR | MR

[11] Yukhnovskii I. R., TMF, 36:3 (1978), 373–399

[12] Kozitsky Yu. V., Renormalization groups in the phase transition scalar models in the collective variable method. General aspects, Preprint ITP-80-107E, ITP, Kiev, 1980

[13] Yukhnovsky I. R., Kozitsky Yu. V., Phase transition generalized hierarchical model in the collective variable method, Preprint ITP-80-60E, ITP, Kiev, 1980 | MR

[14] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, § 15, Nauka, M., 1976 | MR | Zbl

[15] Yukhnovsky I. R., Vakarchuk I. A., Rudavsky Yu. K., $n$-component model. Functional representation and differential form of equations of the renormalization group, Preprint ITP-79-20E, ITP, Kiev, 1979