Abstract
Ornstein-Zernike behavior for Ising models with infinite-range interactions
Y. Aoun, S. Ott, Y. Velenik
Annales de l'Institut Henri Poincaré
60,
167-207
(2024).
We prove Ornstein-Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumptions on the interaction. The main contribution of this work is that the interactions are not assumed to be of finite range. To the best of our knowledge, this is the first proof of OZ asymptotics for a nontrivial model with infinite-range interactions.
Our results actually apply to the Green function of a large class of "self-repulsive in average" models, including a natural family of self-repulsive polymer models that contains, in particular, the self-avoiding walk, the Domb-Joyce model and the killed random walk.
We aimed at a pedagogical and self-contained presentation. Key words: Ising model, Ornstein-Zernike asymptotics, long-range interactions, correlation length, analyticity, coarse-graining, polymers Files: PDF file, Published version, bibtex, slides, talk
Our results actually apply to the Green function of a large class of "self-repulsive in average" models, including a natural family of self-repulsive polymer models that contains, in particular, the self-avoiding walk, the Domb-Joyce model and the killed random walk.
We aimed at a pedagogical and self-contained presentation. Key words: Ising model, Ornstein-Zernike asymptotics, long-range interactions, correlation length, analyticity, coarse-graining, polymers Files: PDF file, Published version, bibtex, slides, talk