## 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

### MSC:

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

### Citations:

Zbl 0378.60107; Zbl 0415.60092; Zbl 0364.60120; Zbl 0404.60096
Full Text:

### References:

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