The paper presents and compares three potential formulations to solve nonlinear static magnetic field problems by applying the fixed-point technique and the Newton-Raphson scheme. Nonlinear characteristics have been handled by the polarization method in the two algorithms. The proposed combination of Newton-Raphson scheme and the polarization formulation result in a very effective nonlinear solver, because only the derivate of the characteristics, i.e. only the permeability or the reluctivity has to be used. That is why, this method can be prosperous to solve nonlinear problems with hysteresis, and it is faster than the classical fixed-point method.