Quark condensate in a magnetic field

We study the dependence of quark condensate $\Sigma$ on an external magnetic field. For weak fields, it rises linearly with the field. Pion mass and residue are also shifted so that the Gell-Mann - Oakes - Renner relation is satisfied. In the strong field region, $\Sigma(H) \propto (eH)^{3/2}$.