We show the validity of the cluster expansion in the canonical ensemble for the Ising model. We compare its radius of convergence with the one computed by the virial expansion working in the grand-canonical ensemble. Using the cluster expansion we give direct proofs with quantification of the higher order error terms for the decay of correlations, central limit theorem and large deviations.
Cluster expansion in the canonical ensemble
Cluster expansions, trees, inversions and correlations
On thermodynamic states of the Ising model on scale-free graphs
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