Exploring mean field spin models with multiple populations: A theoretical framework

Author:

Ansah Richard Kwame12ORCID,Boadi Richard Kena2,Obeng-Denteh William2ORCID,Tawiah Kassim13ORCID,Appiah Sampson Takyi1ORCID

Affiliation:

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

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

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

Abstract

This paper thoroughly investigates the analysis of a modified generalized mean-field Ising model. The thermodynamic limit of free energy is investigated, and both the upper and lower bounds are derived. The lower bound is derived using a standard entropic variational principle, whereas a decoupling method is employed to derive the upper bound. Although the two bounds differ in form, they exhibit the same local maxima. Finally, the impact of a slight external field on the magnetic order is analyzed.

Publisher

AIP Publishing

Reference22 articles.

1. Magnetisation and mean field theory in the Ising model;SciPost Phys. Lect. Notes

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