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 TMF, 1975, Volume 23, Number 3, Pages 366–373 (Mi tmf3911)

Analysis of the nonstar graphs of the Legendre transform in the ising model

A. N. Vasil'ev, R. A. Radzhabov

Abstract: Investigation (started in [1]) of the first Legendre transformation for the logarithm of the statistical sum in the Ising model is continued. The diagram expansion of the Legendre transformation $\Phi$ is the analogue of the virial expansion in the nonideal gas theory, however in contrast to the gas theory, in the case of the Ising model the functional $\Phi$ contains nonstar graphs as well. Complete characterisation of these graphs is given. The practical method of constructing the nonstar graphs (the compensation method) is suggested.

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English version:
Theoretical and Mathematical Physics, 1975, 23:3, 575–579

Citation: A. N. Vasil'ev, R. A. Radzhabov, “Analysis of the nonstar graphs of the Legendre transform in the ising model”, TMF, 23:3 (1975), 366–373; Theoret. and Math. Phys., 23:3 (1975), 575–579

Citation in format AMSBIB
\Bibitem{VasRad75} \by A.~N.~Vasil'ev, R.~A.~Radzhabov \paper Analysis of the nonstar graphs of the Legendre transform in the ising model \jour TMF \yr 1975 \vol 23 \issue 3 \pages 366--373 \mathnet{http://mi.mathnet.ru/tmf3911} \transl \jour Theoret. and Math. Phys. \yr 1975 \vol 23 \issue 3 \pages 575--579 \crossref{https://doi.org/10.1007/BF01041677} 

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This publication is cited in the following articles:
1. 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”, Theoret. and Math. Phys., 26:3 (1976), 230–237
2. G. V. Matvienko, “Critical behavior of the ferromagnetic ising chain with interaction $J_{ij}=|i-j|^{-2}$”, Theoret. and Math. Phys., 63:3 (1985), 635–640
3. G. V. Matvienko, “Critical behavior of a plane Ising antiferromagnet with two-dimensional dipole interaction”, Theoret. and Math. Phys., 69:2 (1986), 1156–1163
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