https://doi.org/10.1140/epjp/s13360-023-04251-3
Regular Article
Inverse problem for the quartic mean-field Ising model
1
Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana
2
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
3
Department of Statistics and Actuarial Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Received:
14
May
2023
Accepted:
4
July
2023
Published online:
18
July
2023
This paper presents a thorough examination of the thermodynamic limit of the pressure function for the mean-field Ising model with four-body interaction. By utilizing a standard entropic variational principle and decoupling method, both upper and lower bounds were derived, and interestingly, these bounds shared the same local maxima. Additionally, the paper explores and solves the inverse problem related to the mean-field Ising model with four-body interaction. We established a connection between the analytical inversion and statistical observations by utilizing the maximum likelihood criteria and creating a relationship between the estimated and theoretical values.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
