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 TMF, 1976, Volume 26, Number 3, Pages 341–351 (Mi tmf3228)

High-temperature expansions at an arbitrary magnetization in the ising model

N. M. Bogolyubov, V. F. Brattsev, A. N. Vasil'ev, A. L. Korzhenevskii, R. A. Radzhabov

Abstract: The first eight orders are calculated in the high-temperature expansion in powers of $\beta=1/kT$ of the function $\varphi(\alpha , \beta)$ ($\alpha$ is the magnetization), which is the Legendre transform of the specific logarithm of the partition function $w$ with respect to the reduced external field $\alpha\equiv\beta h$. This is equivalent to calculating $w$ in an arbitrary external field in temperature-magnetization variables. The transition from the field to the magnetization enables one to use the high-temperature expansion below the Curie point as well, and, in particular, it enables one to calculate the spontaneous magnetization in zero field below the transition point. The calculations are made for two planar (square and triangular) and three three-dimensional (simple cubic, bcc and fcc) lattices, two variants being considered for the three-dimensional lattices: interaction of only nearest neighbors and interaction of first and second neighbors.

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English version:
Theoretical and Mathematical Physics, 1976, 26:3, 230–237

Revised: 13.10.1975

Citation: N. M. Bogolyubov, V. F. Brattsev, A. N. Vasil'ev, A. L. Korzhenevskii, R. A. Radzhabov, “High-temperature expansions at an arbitrary magnetization in the ising model”, TMF, 26:3 (1976), 341–351; Theoret. and Math. Phys., 26:3 (1976), 230–237

Citation in format AMSBIB
\Bibitem{BogBraVas76} \by N.~M.~Bogolyubov, V.~F.~Brattsev, A.~N.~Vasil'ev, A.~L.~Korzhenevskii, R.~A.~Radzhabov \paper High-temperature expansions at an~arbitrary magnetization in the ising model \jour TMF \yr 1976 \vol 26 \issue 3 \pages 341--351 \mathnet{http://mi.mathnet.ru/tmf3228} \transl \jour Theoret. and Math. Phys. \yr 1976 \vol 26 \issue 3 \pages 230--237 \crossref{https://doi.org/10.1007/BF01032093} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. M. Bogolyubov, “Convergence of Feynman diagram expansions in the Ising model”, Theoret. and Math. Phys., 30:1 (1977), 88–90
2. V. V. Borzov, “High-temperature behavior of the partition function for the $P(\varphi)_2$ model of Euclidean field theory”, Theoret. and Math. Phys., 76:3 (1988), 895–903
3. N. M. Bogolyubov, K. L. Malyshev, “Ising limit of a Heisenberg $XXZ$ magnet and some temperature correlation functions”, Theoret. and Math. Phys., 169:2 (2011), 1517–1529
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