Magnetic field induced order in quasi-one-dimensional systems

We investigate possible ordered phases in a magnetic field in quasi-one-dimensional conductors (Q1D$Q1D$). Long ago [I.E. Dzyaloshinskii, E.I. Kats, JETP 28 (1969) 178] we found that sufficiently strong external magnetic field leads to instability of the Fermi state with an arbitrarily weak repulsion between the particles. In the present communication we generalize this idea and provide more details to assign a physical meaning to such a state. We show that without umklapp processes the found instability corresponds to antiferromagnetic (spin density wave) order, whereas umklapp processes favor to Cooper pairing.