Inverse problem for the quartic mean-field Ising model

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.