  Very short quantum wires (quantum contacts) exhibit a conductance structure
at the value of conductance close to 0.7 x 2e^2/h. The structure was discovered
by Thomas et al (Phys. Rev. Lett. {\bf 77}, 135 (1996)). Dependence of the
structure on the longitudinal magnetic field was studied in the same
experiment. This dependence has clearly demonstrated that the effect is related
to the electron spin. In the recent work (Sushkov, Phys. Rev. B {\bf 64},
(2001)) it was suggested that the effect is caused by the development of the
charge density wave within the contact. The many-body Hartree-Fock calculation
has confirmed the picture. The exchange electron-electron interaction is
crucial for this calculation, so in agreement with experiment the effect is
intrinsically related to the spin. However the dependence on the magnetic field
has not been calculated yet. In the present paper the many-body Hartree-Fock
calculation of conductance in the presence of the longitudinal magnetic field
is performed.
