Weighted dependency graphs and the Ising model
  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. 
Jehanne Dousse and Valentin F\'eray
math.PR math-ph math.CO math.MP