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Actually what is given here is not the definition of a Gibbs state, even though stationary distributions of a Markov chain often turn out to be Gibbsian. A gibbs state is particular type of random field with a kind of generalized Markovian structure. A definition of a Gibbs measure (in the case of lattice models) is given on the page on "Gibbs random fields". I think that there should be a single page for "Gibbs state", "Gibbs measure", "Gibbs random field" (and others ?), as these terms are all used interchangeably.