Chiral thermodynamics in a magnetic field

The phase structure of the QCD vacuum in a magnetic field H is investigated at low temperatures T. The free energy of the hadronic phase in a constant homogeneous magnetic field is calculated in the one-loop approximation of chiral perturbation theory. The quark and the gluon condensate are found as functions of temperature and the field strength. It is shown that the order parameter $leftlangle {bar qq} rightrangle $ for the chiral phase transition remains constant when the temperature T and the magnetic field H change in such a way that H=const×T ².