Abstract:
The paper considers a model of a ferromagnet constructed on the basis of the mean field approximation. This model is fully described Curie-Weiss theory within a single implementation (sample).
The concept of the problem of the set of realizations (PMR) is introduced, which arises when the BBGKY hierarhy is closed — an implicit transition from the description ensemble of non interaction samples to the description of one sample.
It is shown that the closure of the BBGKY hierarhy through the mean field approximation leads to TMR. At the same time, the approximation of correlation magnetodynamics makes it possible to avoid PMR and leads to a correct description of the entire ensemble at the level of one-two-particle distribution functions.
Keywords:
mean field approximation, BBGKY hierarhy, correlation magnetodinamics.
Document Type:
Preprint
Language: Russian
Citation:
A. V. Ivanov, S. A. Khilkov, “Mean field approximation and the problem of multiple realizations in the BBGKY hierarchy on the example of a ferromagnet”, Keldysh Institute preprints, 2022, 085, 12 pp.
\Bibitem{IvaKhi22}
\by A.~V.~Ivanov, S.~A.~Khilkov
\paper Mean field approximation and the problem of multiple realizations in the BBGKY hierarchy on the example of a ferromagnet
\jour Keldysh Institute preprints
\yr 2022
\papernumber 085
\totalpages 12
\mathnet{http://mi.mathnet.ru/ipmp3110}
\crossref{https://doi.org/10.20948/prepr-2022-85}
Linking options:
https://www.mathnet.ru/eng/ipmp3110
https://www.mathnet.ru/eng/ipmp/y2022/p85
This publication is cited in the following 2 articles:
Sergei Vladimirovich Zamiatin, Andrey Vladimirovich Lukyanov, Anton Valerievich Ivanov, “On the accuracy of approximation of the two-particle distribution function for a ferromagnet”, KIAM Prepr., 2024, no. 20, 1
S. V. Zamyatin, A. V. Lukyanov, A. V. Ivanov, “O tochnosti approksimatsii dvukhchastichnoi funktsii raspredeleniya dlya ferromagnetika”, Preprinty IPM im. M. V. Keldysha, 2024, 020, 32 pp.
Citation in format AMSBIB
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