Fluctuation results for general block spin Ising models

Understand

We study a block spin mean-field Ising model, i.e.

• a model of spins in which the vertices are divided into a finite number of blocks with each block having a fixed proportion of vertices, and where pair interactions are given according to their blocks.
• For the vector of block magnetizations we prove Large Deviation Principles and Central Limit Theorems under general assumptions for the block interaction matrix.
• Using the exchangeable pair approach of Stein's method we establish a rate of convergence in the Central Limit Theorem for the block magnetization vector in the high temperature regime.