Finite lattice-size effects on QCD thermodynamics

The relationship between continuum perturbation theory and finite-size lattices is studied for QCD at high temperature. This is accomplished by computing the static limit of the gluon self-energy on the lattice to one-loop order. Doing the sum over discrete frequencies analytically permits one to write the result in a very simple form as a threefold sum over the momenta. This expression closely resembles the continuum expression. The plasmon contribution to the pressure of an interacting gluon plasma is estimated on the lattice, and is shown to be greatly suppressed by the finite-size cutoff of lattices presently used in Monte Carlo simulations. The same techniques are used to compare the energy density and the quark number susceptibility for an ideal gas of quarks and gluons, in the continuum and on the lattice. All of the quantities mentioned above are renormalized differently when going from the continuum to a finite-size lattice.