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Annales de l’Institut Henri Poincaré D

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Volume 6, Issue 4, 2019, pp. 533–571
DOI: 10.4171/AIHPD/78

Published online: 2019-09-04

Weighted dependency graphs and the Ising model

Jehanne Dousse[1] and Valentin Féray[2]

(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