1998/12/18 by Sergio Albeverio, Albeverio, Sergio, Yuri Kondratiev +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum many-body systems #Random Matrices and Applications #Theoretical and Computational Physics #math-ph #math.MP #math.OA
paper · pdf · doi:10.48550/arxiv.math-ph/9812017
23 pages, LaTeX, submitted to Letters in Mathematical Physics
arxiv created 1998/12/18 · openalex publication_date 1998/12/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Models of quantum and classical particles on the d-dimensional cubic lattice with pair interparticle interactions are considered. The classical model is obtained from the corresponding quantum one when the reduced physical mass of the particle tends to infinity. For these models, it is proposed to define the convergence of the Euclidean Gibbs states, when the reduced mass tends to infinity, by the weak convergence of the corresponding Gibbs specifications, determined by conditional Gibbs measures. In fact it is proved that all conditional Gibbs measures of the quantum model weakly converge to the conditional Gibbs measures of the classical model. A similar convergence of the periodic Gibbs measures and, as a result, of the order parameters, for such models with the pair interactions possessing the translation invariance, has also been proven.