Relaxed criteria of the Dobrushin-Shlosman mixing condition

Abstract An interacting particle system (Glauber dynamics), which evolves on a finite subset in the integer lattice is considered. It is known that a mixing property of the Gibbs state in the sense of Dobrushin and Shlosman ([DSh85]) is equivalent to several very strong estimates in terms of the Glauber dynamics ([SZ92b]). We show that similar, but seemingly much milder estimates are again equivalent to the Dobrushin-Shlosman mixing condition, hence to the original ones in [SZ92b]. This may be understood as the absence of intermediate speed of convergence to equilibrium.