Applications of the Harris-FKG Inequality to Upper Bounds for Order Parameters in the Contact Processes

Abstract

Upper bounds for order parameters are studied for the d-dimensional contact processes by using the Harris-FKG inequality. Particularly, in the one-dimensional system, it is proved that our improved upper bound ρ_1,λ⁽⁴⁾ is less than Griffeath’s bound for λ≥λ_c(1).