  Application of the magnetic field parallel to the plane of the graphene sheet
leads to the formation of electron- and hole-like Fermi surfaces. Such
situation is shown to be unstable with respect to the formation of an excitonic
condensate even for an arbitrary weak magnetic field and interaction strength.
At temperatures lower than the mean-field temperature the order parameter
amplitude is formed. The order parameter itself is a U(2) matrix allowing for
the combined rotations in the spin and valley spaces. These rotations smoothly
interpolate between site and bond centered spin density waves and spin flux
states. The trigonal warping, short range interactions, and the three particle
Umklapp processes freeze some degrees of freedom at temperatures much smaller
than the mean-field transition temperature and make either
Berezinskii-Kosterlitz-Thouless (driven either by vortices or half-vortices) or
Ising type transitions possible. Strong logarithmic renormalization for the
coupling constants of these terms by the Coulomb interaction are calculated
within one-loop renormalization group. It is found that in the presence of the
Coulomb interaction some short range interaction terms become much greater than
one might expect from the naive dimensionality counting.
