NONEXISTENCE OF PLANAR MAGNETIC ORDER IN THE ONE-DIMENSIONAL AND 2-DIMENSIONAL GENERALIZED HUBBARD-MODEL AT FINITE TEMPERATURES

It is proved that there cannot be planar magnetic order in the generalized Hubbard model in one and two dimensions at finite temperatures. The term "planar magnetic order" is used for any order parameter that confines the spin vectors to a plane. The result holds for ferromagnetism, commensurate or incommensurate antiferromagnetism, canted states, and a wide class of spiral phases. It is also valid for the extended Hubbard model with an arbitrary but finite number of bands, and finite-range hopping. The proof is analogous to the one used by Hohenberg, Mermin and Wagner, and Ghosh.