Low-temperature thermodynamics of the two-dimensional orbital antiferromagnet

We consider the low-temperature properties of a two-dimensional orbital anti-ferromagnet (OAF), which is one of the possible states of the weakly interacting electron system with a half-filled band on a square lattice. Such a state can result from anisotropic electron-hole pairing due to the nesting property of the Fermi surface, and is characterized by nonzero local currents violating translational symmetry of the underlying lattice. Within a simple mean-field model, we show that, in the low-energy limit, the 2D OAF is described by (2+1)-dimensional quantum field theory of gapless fermion excitations associated with zeros of the gap function. The relativistic Landau quantization of the spectrum in external magnetic field shows up in unusual behavior of the magnetic susceptibility. Strong diamagnetism of the OAF is found in the perpendicular field, changing to paramagnetism upon the decreasing of the angle between the field and the plane. When the angle approaches zero, the susceptibility shows an oscillatory angle dependence.