First we obtain the effective anisotropy constant at by the Lagrange multiplier method for each of the thin films that conform the set (for more details about this method see section 2.4). After that, we extract the effective anisotropy constants of the same systems but with the constrained Monte Carlo method at (note that due to the limitation of the method it is impossible to perform simulations of the CMC at ). And finally we compare the effective uniaxial anisotropy constants obtained by both methods. In the case of the Lagrange multiplier method the effective uniaxial anisotropy constant ( ) is calculated from the expression of the energy barrier of the system, in the CMC method from the restoring torque curve.

The results of this test are plotted in Fig. 4.3, the squared dots represent the data obtained by the Lagrange multiplier method and the circular ones are obtained by the CMC method. The value of the effective uniaxial anisotropy constant is normalized by the value of the macroscopic volume anisotropy constant at (). As we can see, the data show total agreement between both methods at low temperature. The results show a linear behavior of the effective anisotropy as a function of ratio as predicted by the formula:
(74) 