Large Deviations for Quantum Spin Systems

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages XΛ := 1 |Λ| ∑ i∈Λ Xi, where the Xi’s are copies of a self-adjoint element X (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of 1 |Λ| ∑ i∈Λ δXi .