Ornstein-Zernike Theory for the finite range Ising models above T_c

2001/11/27 by Massimo Campanino, M. Campanino, Dmitry Ioffe +3 · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:37C30 #msc:60F15 #msc:60K15 #msc:60K35 #msc:82B20

paper · pdf · doi:10.1007/s00440-002-0229-z

published as Probab. Theory Relat. Fields, Vol. 125, Nr. 3 (2003) , p. 305--349 · 36 pages, 5 figures

arxiv created 2001/11/27 · arxiv published 2001/11/27 · openalex publication_date 2003/03/01 · arxiv updated 2011/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• Statistical mechanical methods in particle structure analysis of lattice field theories

Cited by

• Diffraction Spectrum of Lattice Gas Models above T c

Discussions

• Let me discuss this, as you do, in the case of the Ising model. Above the critical temperature, the correlation length in direction $\vec n$ ( $\vec n$ being a unit vector in $\mathbb{R}^d$ ) can be d [stackexchange, 3 points]