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

We present complete three loop results and preliminary four loop results for the 2D O(n) nonlinear sigma model with 0-loop and 1-loop Symanzik improved actions. This calculation aims to test the improvement in the numerical precision that the combination of Symanzik actions and effective couplings can give in Monte Carlo simulations.