Relative Entropy, Gaussian Concentration and Uniqueness of Equilibrium States
Jean-René Chazottes (Institut Polytechnique de Paris)
F.H.J. Redig (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
For a general class of lattice spin systems, we prove that an abstract Gaussian concentration bound implies positivity of the lower relative entropy density. As a consequence, we obtain uniqueness of translation-invariant Gibbs measures from the Gaussian concentration bound in this general setting. This extends earlier results with a different and very short proof.
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