Attractiveness of interactions for binary lattice systems and the global Markov property (Q1098181)

The author gives a necessary and sufficient condition for the nearest neighbor pair interaction to be attractive with respect to some order on the states of binary lattice systems. In virtue of \textit{H. Fölmer}'s recent result on attractive interactions [Quantum fields-algebras, processes, Proc. Symp., Bielefeld 1978, 293-302 (1980; Zbl 0457.60077)], this implies that if a nearest neighbor translation invariant interaction on a square lattice generates a unique Gibbs state, the latter possesses the global Markov property.