Four-loop free energy for the 2D O(n) nonlinear sigma-model with 0-loop and 1-loop Symanzik improved actions

We calculate up to four loops the free energy of the two-dimensional (2D) O(n) nonlinear sigma-model regularized on the lattice with the 0-loop and 1-loop Symanzik improved actions. An effective coupling constant based on this calculation is defined.