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Possible Fermi-surface-related instabilities in a Hubbard model, generalized so as to include finite-range and exchange interactions, are studied in the weak-coupling limit. In addition to the usual instabilities of superconducting, charge- or spin-density-wave type, two new types of instability are found. The first state is an orbital antiferromagnet, with currents circulating around each elementary plaquette. In the second phase, a spin current flows around the plaquettes. In both cases, there are low-temperature power laws in thermodynamic and transport properties. Two-dimensional fluctuation effects are shown to lead, for weak interactions, to a sharp crossover from a Fermi-liquid state to a regime governed by orientational fluctuations of the order parameter at fixed amplitude.
H. J. Schulz (1989) studied this question.