Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model

Francesco Camilli, Emanuele Mingione and Godwin Osabutey ()
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Francesco Camilli: Quantitative Life Sciences, International Centre for Theoretical Physics, 34151 Trieste, Italy
Emanuele Mingione: Department of Matematics, Alma Mater Studiorum, University of Bologna, 40126 Bologna, Italy
Godwin Osabutey: Department of Matematics, Alma Mater Studiorum, University of Bologna, 40126 Bologna, Italy

Mathematics, 2025, vol. 13, issue 8, 1-25

Abstract: We study the thermodynamic properties of the generalized non-convex multispecies Curie–Weiss model, where interactions among different types of particles (forming the species) are encoded in a generic matrix. For spins with a generic prior distribution, we compute the thermodynamic limit of the generating functional for the moments of the Boltzmann–Gibbs measure using simple interpolation techniques. For Ising spins, we further analyze the fluctuations of the magnetization in the thermodynamic limit under the Boltzmann–Gibbs measure. It is shown that a central limit theorem (CLT) holds for a rescaled and centered vector of species magnetizations, which converges to either a centered or non-centered multivariate normal distribution, depending on the rate of convergence of the relative sizes of the species.

Keywords: non-convex Curie–Weiss model; central limit theorem; Ising model; multispecies mean-field model; arbitrary spin distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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