Robustness of the non-Gibbsian property: some examples

We discuss some examples of measures on lattice systems, which lack the property of being a Gibbs measure in a rather strong sense. 1 Introduction In recent years extensive research has been done on the occurrence of states (probability measures) on lattice systems which are not of Gibbsian type. Such measures occur for example in renormalization-group studies [17, 18, 21, 8, 9, 10, 11, 12, 13, 40], non-equilibrium statistical mechanical models [42, 26, 33, 38], image analysis [5, 15, 34], probabilistic cellular automata [25, 33] and random cluster models [19, 39]. The possibility of their occurrence and their properties have been considered by various authors [1, 7, 14, 20, 22, 24, 28, 29, 30, 31, 32, 36, 37, 41, 44]. This non-Gibbsian behaviour has often been considered `pathological' --- undesirable ---, and there have been various attempts to control the nonGibbsianness. One approach, advocated by Martinelli and Olivieri [36, 37], is to study how the non-Gibbsian measures behav..