Abstract

Ornstein-Zernike Theory for Finite Range Ising Models Above $T_{\rm c} M. Campanino, D. Ioffe and Y. Velenik Probab. Theory Relat. Fields 125 305-349 (2003). We derive precise Ornstein-Zernike asymptotic formula for the decay of the two-point function in the general context of finite range Ising type models on $\mathbb{Z}^d$. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and, by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in the whole of the high temperature region $T>T_{\rm c}$. As a byproduct we obtain that for every $T>T_{\rm c}$, the inverse correlation length is an analytic and strictly convex function of direction. Key words: Ising model, Ornstein-Zernike decay of correlations, Ruelle operator, renormalization, local limit theorems. Files: PDF file, Published version, bibtex