EXPONENTIAL RELAXATION OF GLAUBER DYNAMICS WITH SOME SPECIAL BOUNDARY-CONDITIONS

We consider attractive finite-range Glauber dynamics and show that if a certain mixing condition is satisfied, then the system evolving on a rbitrary subsets of the lattice, with appropriate boundary conditions, converges to equilibrium exponentially fast, in the uniform sense, un iformly over the subsets of the lattice. This result applies, for inst ance, to the ferromagnetic nearest neighbor Ising model in the so-call ed ''Basuev region,'' where complete analyticity is expected to fail. Technically the result in this paper is an extension of a result of Ma rtinelli and Olivieri, who proved that under a weaker form of mixing t he infinite system approaches equilibrium exponentially fast. Conceptu ally this paper may be seen as a step towards developing and exploitin g a restricted notion of complete analyticity in which the boundary co nditions, rather than the shapes of the regions under consideration, a re being restricted.