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On the possible failure of the Gibbs propertyfor measures on lattice systemsAernout

We review results which have been obtained in the last few years on the topic whether various measures of physical interest, deened on lattice systems, have the Gibbs property or not. Most of the measures we consider occur either within renormalization-group theory or within models of non-equilibrium statistical mechanics. In renormalization-group theory examples we discuss in particular the uniqueness regime and the critical regime. Moreover we consider the question how severely the Gibbs property is violated in various examples.