Abstract:
The link between Bogoiyubov's statistical variational principle for free energy, the method
of partial diagram summation of the perturbation theory, and the Luttinger–Ward theorem
is established. On the basis of Matsubara's Green's function method the nonlinear integral
Dyson equation is solved by approximating the effective potential and a new implicit equation
of magnetic state is obtained for the Ising model.
Citation:
Yu. G. Rudoi, “Bogolyubov's statistical variational principle and the Green's function method applied to the Heisenberg–Ising model”, TMF, 2:1 (1970), 129–148; Theoret. and Math. Phys., 2:1 (1970), 98–112
\Bibitem{Rud70}
\by Yu.~G.~Rudoi
\paper Bogolyubov's statistical variational principle and the Green's function method applied to the Heisenberg--Ising model
\jour TMF
\yr 1970
\vol 2
\issue 1
\pages 129--148
\mathnet{http://mi.mathnet.ru/tmf3995}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 2
\issue 1
\pages 98--112
\crossref{https://doi.org/10.1007/BF01028861}
Linking options:
https://www.mathnet.ru/eng/tmf3995
https://www.mathnet.ru/eng/tmf/v2/i1/p129
This publication is cited in the following 3 articles:
A. L. Kuzemsky, “Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems”, Int. J. Mod. Phys. B, 29:18 (2015), 1530010
Yu. G. Rudoi, Yu. A. Tserkovnikov, “Single-particle Green's function in an anisotropic Heisenberg model”, Theoret. and Math. Phys., 14:1 (1973), 75–89
Yu. A. Tserkovnikov, “Calculation of correlation functions in the ising model with long-range interaction”, Theoret. and Math. Phys., 11:3 (1972), 588–600
Citation in format AMSBIB
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