Ornstein-Zernike theory for finite range Ising models above T c

• DOI: 10.1007/s00440-002-0229-z
• Publication Date: 2004-10-14T23:18:00Z
• Authors: Massimo Campanino; Dmitry Ioffe; Y van Velenik
• Keywords: Statistical Mechanics (cond-mat.stat-mech); Probability (math.PR); 0103 physical sciences; FOS: Mathematics; FOS: Physical sciences; Mathematical Physics (math-ph); 60F15, 60K15, 60K35, 82B20, 37C30; 0101 mathematics; 01 natural sciences; Mathematics - Probability; Condensed Matter - Statistical Mechanics; Mathematical Physics

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 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 Fernandez, goes through in the whole of the high temperature region T > T_c. As a byproduct we obtain that for every T > T_c, the inverse correlation length is an analytic and strictly convex function of direction.<br/>36 pages, 5 figures<br/>