The quark-hadron thermodynamics in magnetic field

Nonperturbative treatment of quark-hadron transition at nonzero temperature T and chemical potential mu in the framework of Field Correlator Method is generalized to the case of nonzero magnetic field B. A compact form of the quark pressure for arbitrary B, mu, T is derived. As a result the transition temperature is found as a function of B and mu, which depends on only parameters: vacuum gluonic condensate G_2 and the field correlator D_1^E(x), which defines the Polyakov loops and it is known both analytically and on the lattice. A moderate (25%) decrease of T_c(mu=0) for eB changing from zero to 1 GeV^2 is found. A sequence of transition curves in the (mu, T) plane is obtained for B in the same interval, monotonically decreasing in scale for growing B.