Limit theorems for the empirical vector of the Curie-Weiss-Potts model
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 \textit{R. S. Ellis, C. M. Newman} and \textit{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.
scientific article; zbMATH DE number 4157590
scientific article