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Dal'nevostochnyi Matematicheskii Zhurnal, 2019, Volume 19, Number 2, Pages 235–244 (Mi dvmg411)  
An accelerated exhaustive enumeration algorithm in the Ising model

M. A. Padalkoab, P. D. Andriushchenkoa, K. S. Soldatova, K. V. Nefedevab

a Far Eastern Federal University, Vladivostok
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
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Abstract: An accelerated algorithm for the precise calculation of the lattice Ising model is presented. The algorithm makes it possible to calculate two-dimensional 8$\times$8 lattices for periodic boundary conditions on ordinary personal computers. In turn, the exact solution obtained by the proposed method makes it possible to check the effectiveness of various probabilistic approaches, in particular the Monte Carlo methods. The algorithm is applicable to various types of lattices.
Key words: Izing model, complete enumeration, Monte-Carlo method.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-00400-19-01
The work was supported by the Ministry of Science and Higher Education. State assignment number 075-00400-19-01.
Received: 17.07.2019
Document Type: Article
UDC: 517.5
MSC: Primary 30A10; Secondary 30C10, 30C15
Language: Russian
Citation: M. A. Padalko, P. D. Andriushchenko, K. S. Soldatov, K. V. Nefedev, “An accelerated exhaustive enumeration algorithm in the Ising model”, Dal'nevost. Mat. Zh., 19:2 (2019), 235–244
Citation in format AMSBIB
\Bibitem{PadAndSol19}
\by M.~A.~Padalko, P.~D.~Andriushchenko, K.~S.~Soldatov, K.~V.~Nefedev
\paper An accelerated exhaustive enumeration algorithm in the Ising model
\jour Dal'nevost. Mat. Zh.
\yr 2019
\vol 19
\issue 2
\pages 235--244
\mathnet{http://mi.mathnet.ru/dvmg411}
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