Thermodynamics of the two--dimensional O(3) non linear sigma model with Fixed-Point lattice action

We calculate the free energy density of the two dimensional O(3) non linear sigma model over a large temperature region. At high temperatures the calculations could be done by perturbation theory whereas in the low temperature regime we used Monte-Carlo simulations. Using the Fixed–Point action the results do not show any remarkable cut-off effects and furthermore the behaviour of these effects is nearly the same over the whole temperature region. The results of the Fixed-Point action are then compared to those of the standard Wilson action.