Advancing the inverse problem in statistical mechanics: A five-body interaction perspective

Richard Kwame Ansah, Kassim Tawiah and Ruth Naayi Odankey Abbey

Physica A: Statistical Mechanics and its Applications, 2025, vol. 674, issue C

Abstract: This paper explores the inverse Ising problem with five-body interactions in the mean-field model, focusing on deriving analytical solutions and statistical estimations for macroscopic parameters like magnetization and susceptibility. Using the maximum likelihood criterion and clustering algorithms, the study presents a robust framework for parameter estimation that addresses challenges posed by metastable states. Results demonstrate the convergence of finite-size quantities to their thermodynamic counterparts, providing insights into higher-order interactions’ roles in statistical mechanics. This approach offers significant applications in physics, biological systems, and data science, enriching the theoretical and practical toolkit for addressing complex inverse problems.

Keywords: External field; Decoupling; Five-body interaction; Inverse problem (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125003528

DOI: 10.1016/j.physa.2025.130700

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