Nonperturbative quark-gluon thermodynamics at finite density

Thermodynamics of the quark-gluon plasma at finite density is studied in the framework of the Field Correlator Method, where thermodynamical effects of Polyakov loops and colormagnetic confinement are taken into account. Having found good agreement with numerical lattice data for zero density, we calculate pressure $P(T,\,\mu)$ for $0 <\mu< 400$ MeV and $150 <T< 1000$ MeV. For the first time the explicit intergral form is found in this region,demonstrating analytic structure in the complex $\mu$ plane. The resulting multiple complex branch points are found at the Roberge-Weiss values of $\operatorname{Im}\,\mu$, with $\operatorname{Re}\,\mu$ defined by the values of Polyakov lines and colormagnetic confinement.