STOCHASTIC MONOTONICITY AND POSITIVE CORRELATIONS OF SPIN SYSTEMS

In this paper, we discuss spin systems on the product space\prod_u \in \mathcalS 0, 1, …, N_u,get a necessary and sufficient condition for the stochastic monotonicity of systems, and give a necessary condition for positive correlations of systems with the "two point measure" method. In particularly, we prove the equivalence property of stochastic monotonicity and positive correlations of spin systems on 0, 1^s.