We analyze the high temperature fluctuations of the magnetization of the so-called Ising block model. This model was recently introduced by Berthet et al. in . We prove a Central Limit Theorems (CLT) for the magnetization in the high temperature regime. At the same time we show that this CLT breaks down at a line of critical temperatures. At this line we prove a non-standard CLT for the magnetization.
"Fluctuations for block spin Ising models." Electron. Commun. Probab. 23 1 - 12, 2018. https://doi.org/10.1214/18-ECP161