Long-range orbital order in a degenerate-orbital Hubbard model: absence in low-dimensions

We investigate the possibility of long range orbital order in low-dimensional systems. The study is performed within a two-orbital Hubbard model by means of the Bogoliubov's inequality. We show that, in one- and two-dimensions, and when a narrow conduction band is concerned, this model does not exhibit orbital order at any filling and any finite temperature.