Upper and Lower Bounds for Canonical Ensemble Averages

Abstract

Upper and lower bounds are obtained for canonical ensemble averages. The bounds are expressed entirely in terms of averages with respect to an arbitrary unperturbed canonical ensemble density operator. A weak form of the derived bounds is used to show that, for magnetic fields exceeding a given critical value, the magnetization of the antiferromagnetic linear chain approaches ferromagnetic saturation as the temperature approaches absolute zero.