Quark-hadron thermodynamics in a magnetic field

Nonperturbative treatment of the quark- hadron transition at nonzero temperature T and chemical potential mu in the framework of the 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 only on the following parameters: the vacuum gluonic condensate G(2) and the field correlator D-1(E) (x), which defines the Polyakov loops and is known both analytically and on the lattice. A moderate (25%) decrease of T-c (mu = 0) for eB changing from zero to 1 GeV2 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.