COUPLING SURFACES AND WEAK BERNOULLI IN ONE AND HIGHER DIMENSIONS

We propose a notion of weak Bernoulli in all dimensions which generali zes the usual definition in dimension I. The key idea is the concept o f a coupling surface. We relate this notion to previously studied prop erties and discuss a number of possible variants in dimension 1. We al so show that the Ising model, at low temperature, is weak Bernoulli wi th an explicit description of the coupling surface. (C) 1997 Academic Press.