Magnetic properties of some itinerant-electron systems at T>0

The Lieb-Mattis theorem on the absence of one-dimensional ferromagnetism is extended here from ground states to T>0 by proving, inter alia, that M the magnetization of a quantum system in a field h>0, is always less than the pure paramagnetic value M0=tanh with =1/kT. Our proof rests on a new formulation in terms of path integrals that holds in any dimension; another of its applications is that the Nagaoka-Thouless theorem on the Hubbard model also extends to T>0 in the sense that Mexceeds M0.