Gaussian Concentration and Uniqueness of Equilibrium States in Lattice Systems
J.R. Chazottes (Institut Polytechnique de Paris)
J. Moles (Autonomous University of San Luis Potosí, Institut Polytechnique de Paris)
F. Redig (TU Delft - Applied Probability)
E. Ugalde (Autonomous University of San Luis Potosí)
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Abstract
We consider equilibrium states (that is, shift-invariant Gibbs measures) on the configuration space SZd where d≥ 1 and S is a finite set. We prove that if an equilibrium state for a shift-invariant uniformly summable potential satisfies a Gaussian concentration bound, then it is unique. Equivalently, if there exist several equilibrium states for a potential, none of them can satisfy such a bound.