GLOBAL SPECIFICATIONS AND NONQUASILOCALITY OF PROJECTIONS OF GIBBS MEASURES

We study the question of whether the quasilocality (continuity, almost Markovianness) property of Gibbs measures remains valid under a proje ction on a sub-sigma-algebra. Our method is based on the construction of global specifications, whose projections yield local specifications for the projected measures. For Gibbs measures compatible with monoto nicity preserving local specifications, we show that the set of config urations where quasilocality is lost is an event of the tail field. Th is set is shown to be empty whenever a strong uniqueness property is s atisfied, and of measure zero when the original specification admits a single Gibbs measure. Moreover, we provide a criterion for nonquasilo cality (based on a quantity related to the surface tension). We apply these results to projections of the extremal measures of the Ising mod el. In particular, our nonquasilocality criterion allows us to extend and make more complete previous studies of projections to a sublattice of one less dimension (Schonmann example).