Abstract:
The Ising model with a large number z of interacting neighbors is considered. A perturbation theory is constructed on the basis of the method of steepest descents, and it is used to
obtain asymptotic estimates for the correlation functions in any order in 1/z. The temperature dependence of the correlation functions is investigated in the lowest approximations.
Citation:
Yu. A. Tserkovnikov, “Calculation of correlation functions in the ising model with long-range interaction”, TMF, 11:3 (1972), 385–402; Theoret. and Math. Phys., 11:3 (1972), 588–600
\Bibitem{Tse72}
\by Yu.~A.~Tserkovnikov
\paper Calculation of correlation functions in the ising model with long-range interaction
\jour TMF
\yr 1972
\vol 11
\issue 3
\pages 385--402
\mathnet{http://mi.mathnet.ru/tmf2878}
\transl
\jour Theoret. and Math. Phys.
\yr 1972
\vol 11
\issue 3
\pages 588--600
\crossref{https://doi.org/10.1007/BF01028376}
Linking options:
https://www.mathnet.ru/eng/tmf2878
https://www.mathnet.ru/eng/tmf/v11/i3/p385
This publication is cited in the following 6 articles:
M. A. Popov, “Gaussian approximation in the Ising model with long-range interaction”, Theoret. and Math. Phys., 83:3 (1990), 658–663
V. E. Zobov, “Autocorrelation function of a Heisenberg paramagnet in the approximation of a self-consistent fluctuating field”, Theoret. and Math. Phys., 77:3 (1988), 1299–1309
B.E. Vugmeister, V.A. Stephanovich, “New random field theory for the concentrational phase transitions with appearance of long-range order. Application to the impurity dipole systems”, Solid State Communications, 63:4 (1987), 323
D. A. Garanin, V. S. Lutovinov, “Quasi-Taylor series in the theory of magnetism”, Theoret. and Math. Phys., 62:2 (1985), 177–183
Yu. G. Rudoi, “Low-temperature collective Greens's function and longitudinal susceptibility of an anisotropic Heisenberg ferromagnet”, Soviet Journal of Low Temperature Physics, 5:4 (1979), 176
S. I. Kubarev, “Random field method in statistical mechanics”, Theoret. and Math. Phys., 22:1 (1975), 50–58
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