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Inverse problem for the quartic mean-field Ising model

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Abstract

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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Acknowledgements

The authors thank the staff at the Mathematics and Statistics Department of University of Energy and Natural Resources, Department of Statistics and Actuarial Science, Kwame Nkrumah University of Science and Technology, and Department of Mathematics, Kwame Nkrumah University of Science and Technology for their support and kindness during the period this paper was written.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana

    Richard Kwame Ansah & Kassim Tawiah

  2. Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Richard Kwame Ansah, Richard Kena Boadi & William Obeng-Denteh

  3. Department of Statistics and Actuarial Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Kassim Tawiah

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  1. Richard Kwame Ansah
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  2. Richard Kena Boadi
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Ansah, R.K., Boadi, R.K., Obeng-Denteh, W. et al. Inverse problem for the quartic mean-field Ising model. Eur. Phys. J. Plus 138, 626 (2023). https://doi.org/10.1140/epjp/s13360-023-04251-3

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