Fluctuations for block spin Ising models

Understand

We analyze the high temperature fluctuations of the magnetization of the so-called Ising block model.

• This model was recently introduced by Berthet, Rigollet and Srivastava.
• 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.