Abstract
Thermodynamics of the quark-gluon plasma at finite density is studied with the vacuum correlator method. The contribution of the nonperturbative effects is defined by the Polyakov loops and colormagnetic confinement. An analytical expression was obtained for the equation of state $P(T,\mu)$ for $0 < \mu < 400 \ MeV$ in a good agreement with current lattice data at zero density. A set of branching points were found for the $P(T,\mu)$ in a complex $\mu$-plane which coincide with the Roberge-Weiss singularities.
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