  A detailed study of the thermodynamics of the O(N=3) model in 1+1 dimensions
is presented, employing a two-particle-irreducible resummation prescription as
well as fully nonperturbative finite-temperature lattice simulations. The
analytical results are computed using the Cornwall-Jackiw-Tomboulis (CJT)
formalism and the auxiliary field method to one- and to two-loop order. The
lattice results are obtained through Monte Carlo simulation for various lattice
spacings. The analytical and lattice results for pressure, trace anomaly, and
energy density, resembling closely those of four-dimensional Yang-Mills
theories, are compared with each other. We find that to one-loop order there is
a good correspondence between the CJT formalism and the lattice study for low
temperatures. However, at high T the two-loop calculation fares better,
correcting for the overestimation from the former approximation.
