Magnetic properties of some itinerant-electron systems atT>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(β,h), the magnetization of a quantum system in a field h>0, is always less than the pure paramagnetic value ${\mathit{M}}_0$(β,h)=tanh(βh), with β==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 M(β,h) exceeds ${\mathit{M}}_0$(β,h).