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Dal'nevostochnyi Matematicheskii Zhurnal, 2019, Volume 19, Number 2, Pages 245–255
(Mi dvmg412)
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Solution of one-dimensional lattice gas models
Yu. N. Kharchenko Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
Abstract:
In this paper it is shown that the thermodynamic limit of the partition function of the statistical models under
consideration on a one-dimensional lattice with an arbitrary finite number of interacting neighbors is expressed in
terms of the principal eigenvalue of a matrix of finite size. The high sparseness of these matrices for any number of
interactions makes it possible to perform an effective numerical analysis of the macro characteristics of these models.
Key words:
Ising model, transfer matrix, statistical sum, free energy, singular curves, phase transitions.
Received: 16.09.2019
Citation:
Yu. N. Kharchenko, “Solution of one-dimensional lattice gas models”, Dal'nevost. Mat. Zh., 19:2 (2019), 245–255
Linking options:
https://www.mathnet.ru/eng/dvmg412 https://www.mathnet.ru/eng/dvmg/v19/i2/p245
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