Limit theorems for the empirical vector of the Curie-Weiss-Potts model. (English) Zbl 0705.60027

Limit theorems for the empirical vector \(L_ n\) of spin random variables with a parameter of dependence \(\beta\) in the Curie-Weiss-Potts-Ising model of statistical mechanics in both non-critical and critical cases are obtained, including some earlier results of R. S. Ellis, C. M. Newman and J. S. Rosen [Z. Wahrscheinlichkeitstheorie Verw. Gebiete 44, 117-139 (1978; Zbl 0364.60120), and ibid. 51, 153-169 (1980; Zbl 0404.60096)].
The limit theorems state the law of large numbers \(L_ n\to \delta_{\nu^ 0}\), \(n\to \infty\), with \(\nu^ 0=(q^{-1},...,q^{- 1})\), and the number of spin states q, in the sub-critical case \(\beta <\beta_ C\), and its breakdown in critical and super-critical cases \(\beta \geq \beta_ C\), and the central limits for (\(\sqrt{n}L_ n)\) compensated.
Reviewer: E.I.Trofimov


60F05 Central limit and other weak theorems
82B05 Classical equilibrium statistical mechanics (general)
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