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

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.