Annales de l’Institut Henri Poincaré D
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Published online: 2019-09-04
Weighted dependency graphs and the Ising modelJehanne Dousse and Valentin Féray (1) Universität Zürich, Switzerland and Université de Lyon, Villeurbanne, France
(2) Universität Zürich, Switzerland
Weighted dependency graphs have been recently introduced by the second author, as a toolbox to prove central limit theorems. In this paper, we prove that spins in the $d$-dimensional Ising model display such a weighted dependency structure. We use this to obtain various central limit theorems for the number of occurrences of local and global patterns in a growing box.
Keywords: Ising model, cumulants, central limit theorems, cluster expansions, weighted dependency graphs
Dousse Jehanne, Féray Valentin: Weighted dependency graphs and the Ising model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), 533-571. doi: 10.4171/AIHPD/78