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TMF, 1973, Volume 15, Number 3, Pages 407–416 (Mi tmf3680)  

Perturbation theory with variational parameter. Inequalities and estimates for the free energy

N. A. Potapkov


Abstract: A perturbation theory scheme is proposed on the basis of a representation of the free energy as a sequence $F_k(\sigma_k)$ ($\sigma_k$ is the ordering parameter). From the condition of a minimum of $F_k(\sigma_k)$ an equation of state is obtained and a phase transition temperature $T_c^{(k)}$ is determined. For the Heisenberg and Ising models $F_2$ is calculated ($F_1$ is the well-known molecular-field approximation) and the inequality $F_1>F_2>F$ (for the Istng model) is obtained, which shows that $F_2$ is a better approximation than $F_1$. The temperature $T_c^{(2)}$ is also determined for both models. The behavior of the expansion for the free energy as $T\to0$ is investigated.

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English version:
Theoretical and Mathematical Physics, 1973, 15:3, 614–620

Received: 28.06.1972

Citation: N. A. Potapkov, “Perturbation theory with variational parameter. Inequalities and estimates for the free energy”, TMF, 15:3 (1973), 407–416; Theoret. and Math. Phys., 15:3 (1973), 614–620

Citation in format AMSBIB
\Bibitem{Pot73}
\by N.~A.~Potapkov
\paper Perturbation theory with variational parameter. Inequalities and estimates for the free energy
\jour TMF
\yr 1973
\vol 15
\issue 3
\pages 407--416
\mathnet{http://mi.mathnet.ru/tmf3680}
\transl
\jour Theoret. and Math. Phys.
\yr 1973
\vol 15
\issue 3
\pages 614--620
\crossref{https://doi.org/10.1007/BF01094569}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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