Geodesic
Gaussian approximation in the Ising model with long-range interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 3, pp. 455-461 
M. A. Popov. Gaussian approximation in the Ising model with long-range interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 3, pp. 455-461. http://geodesic.mathdoc.fr/item/TMF_1990_83_3_a12/
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     author = {M. A. Popov},
     title = {Gaussian approximation in~the {Ising} model with long-range interaction},
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     pages = {455--461},
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     volume = {83},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_83_3_a12/}
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The infinite hierarchy of equations for the cumulants of the correlation functions of the longitudinal spin components in the Ising model with long-range interaction corresponding to a Gaussian form of the spectral density is investigated. The invariance of the cumulants with respect to permutation of the vertices is used to decouple the hierarchy. A phase transition of the second kind is described by the obtained system of equations for the cumulants of the first three orders in a three-dimensional model.

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