The SU (3) equation of state (P (T ), s(T ), I(T )) are calculated within the Field Correlator Method both in the confined and the deconfined phases. The basic dynamics in our approach is contained in the vacuum correlators, both of the colorelectric (CE) and colormagnetic (CM) types, which ensure CE and CM confinement below T c and CM confinement and Polyakov loops above T c . The resulting values of T c and P (T ), I(T ), s(T ) are in good agreement with lattice measurements. * agasian@itep.ru † lukashov@phystech.edu ‡ simonov@itep.ru

Polyakov loops $L_a(T), a=3,8,...$ are shown to give the most important nonperturbative contribution to the thermodynamic potentials. Derived from the gluonic field correlators they enter as factors into free energy. It is shown in the $SU(3)$ case that $L_a (T)$ define to a large extent the behavior of the free energy and the trace anomaly $I(T)$, most sensitive to nonperturbative effects.Comment: 8 pages, 2 figures; v2: minor corrections, style changed and references adde

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 color magnetic confinement are taken into account. Having found good agreement with numerical lattice data for zero density, we calculate pressure [Formula: see text], for [Formula: see text] MeV and [Formula: see text] MeV. For the first time, the explicit integral form is found in this region, demonstrating analytic structure in the complex [Formula: see text] plane. The resulting multiple complex branch points are found at the Roberge–Weiss values of [Formula: see text], with [Formula: see text] defined by the values of Polyakov lines and color magnetic confinement.

Nonperturbative effects in the quark-gluon thermodynamics are studied in the framework of Vacuum Correlator Method. It is shown, that two correlators: colorelectric D E 1 (x) and colormagnetic D H (x), provide the Polyakov line and the colormagnetic confinement in the spatial planes respectively. As a result both effects produce the realistic behavior of P (T ) and s(T ), being in good agreement with numerical lattice data. * lukashov@phystech.edu † simonov@itep.ru