The Curie temperature is the temperature beyond which a ferromagnetic material becomes paramagnetic and perhaps the loss of the ferromagnetic character with the temperature is the most important temperature effect in magnetic systems. For this reason, to determine the Curie temperature through the constrained Monte Carlo method is a good test. The Curie temperature is related to the value of the exchange constant and in the Mean Field Approximation (MFA) it could be expressed as follows:
We have considered two systems: a bulk system with periodic boundary conditions in with a simple cubic or fcc lattice and evaluated the magnetization as a function of the temperature. We consider that the Curie temperature is defined when the magnetization becomes zero (see Fig. 4.2), excluding the finite-size effects. The exchange constants in both systems are different. In the case of a simple cubic lattice, each spin has 6 first neighbors, the exchange constant is and the Curie temperature obtained by the constrained Monte-Carlo simulation is close to . For a thin film with fcc lattice with a , the number of first neighbors is and the Curie temperature determined by (CMC) simulations is close to .
The Curie temperature obtained by the constrained Monte Carlo
simulation for sc and fcc thin films presents an important discrepancy
with the theoretical Mean Field prediction. In contrast, our values of are in a good agreement with the
values predicted by the classical spectral density method  (see Table 4.2).