Thermodynamics of SU(3) gauge theory in 2+1 dimensions

The pressure, and the energy and entropy densities are determined for the SU(3) gauge theory in 2+1 dimensions from lattice Monte Carlo calculations in the interval 0.6⩽T/Tc⩽15. The finite temperature lattices simulated have temporal extent Nτ=2, 4, 6 and 8, and spatial volumes NS2 such that the aspect ratio is NS/Nτ=8. To obtain the thermodynamical quantities, we calculate the averages of the temporal plaquettes Pτ and the spatial plaquettes PS on these lattices. We also need the zero temperature averages of the plaquettes P0, calculated on symmetric lattices with Nτ=NS. We discuss in detail the finite size (NS-dependent) effects. These disappear exponentially. For the zero temperature lattices we find that the coefficient of NS in the exponent is of the order of the glueball mass. On the finite temperature lattices it lies between the two lowest screening masses. For the aspect ratio equal to eight, the systematic errors coming from the finite size effects are much smaller than our statistical errors. We argue that in the continuum limit, at high enough temperature, the pressure can be parametrized by the very simple formula p=T3(a−bTc/T) where a and b are two constants. Using the thermodynamical identities for a large homogeneous system, this parametrization then determines the other thermodynamical variables in the same temperature range.