Thermodynamics of the two-dimensional O(3) σ-model with fixed-point lattice action

The free energy density of the two-dimensional O(3) non-linear σ-model is calculated at finite temperature and finite spatial extent. Both an analytic calculation in the perturbative regime and a Monte Carlo study at low temperatures are presented. It is shown that using the fixed-point action instead of the standard Wilson action leads to a substantial reduction of the cut-off effects.