4 Tests of the method

Given the originality of the constrained Monte Carlo method, it is important to ensure that the method is reliable and conforms with existing results. For this purpose we have done several tests:

• We have checked that with this method we are able to reproduce the correct Tc of several systems.
• We have checked that the anisotropy constants obtained by the constrained Monte Carlo method at low temperatures are in agreement with those obtained by the Lagrange Multiplier technique at $T=0$ (see previous chapter).
• We have checked that the scaling behavior ( $K\sim M^{\gamma}$) for thin films with pure (uniaxial or cubic) anisotropy at low temperatures obtained by the CMC method are consistent with those predicted by the Callen-Callen theory.