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 Φ 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 Φ 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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/tmf3911
https://www.mathnet.ru/eng/tmf/v23/i3/p366
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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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N. M. Bogoliubov, “Some results of the hightemperature expansions for the Ising model in arbitrary magnetic field”, J. Soviet Math., 23:4 (1983), 2379–2389
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