Quark-hadron thermodynamics in a magnetic field

Abstract

Nonperturbative treatment of the quark-hadron transition at nonzero temperature $T$ and chemical potential $\ensuremath{\mu}$ 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 $B,\ensuremath{\mu},T$ is derived. As a result, the transition temperature is found as a function of B and $\ensuremath{\mu}$, 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 ${T}_{c}(\ensuremath{\mu}=0)$ for $eB$ changing from zero to $1\text{ }\text{ }{\mathrm{GeV}}^{2}$ is found. A sequence of transition curves in the $(\ensuremath{\mu},T)$ plane is obtained for $B$ in the same interval, monotonically decreasing in scale for growing $B$.