Etude des films minces par la méthode de Monte Carlo dans le cadre du modèle de spin d’Ising.

Abstract

Using Monte Carlo simulations, we have studied the critical behaviours and phase diagrams of the spin-1/2 and spin-1 Ashkin Teller model ferromagnetic thin films. In the first part: The effect of the interaction with the exchange coupling 𝐽4 is studied. The phase diagrams present different ratios of the surface exchange interaction at the special point, in which all the films thickness have the same critical temperature. First and second order transitions appears in the system. Moreover, at the special point descriptions, we found another partially ordered phase for certain values of the parameter’s interaction. Finally, the critical exponents of the surface magnetization 𝛽1𝑚 are estimated. In the second part, the effects of the crystal field 𝐷 𝐽 ⁄ 2𝑏 and four-spins coupling (𝐽4𝑠 𝐽 ⁄ 2𝑏, 𝐽4𝑏 𝐽 ⁄ 2𝑏) has been studied in details. The phase diagrams in the (𝑘𝐵𝑇𝑐 𝐽 ⁄ 2𝑏 ,𝐽2𝑠 𝐽 ⁄ 2𝑏) plane exhibits the special point, for different values of 𝐷 𝐽 ⁄ 2𝑏 and (𝐽4𝑠 𝐽 ⁄ 2𝑏, 𝐽4𝑏 𝐽 ⁄ 2𝑏). Then, we found rich phase diagrams with firstand second-order phase transitions that meet at tricritical points, that are depended on the film thickness N. Finally, this model presents a new partially ordered phase < 𝜎𝑆 >, between the paramagnetic phase and the Baxter phase, which are separated by a second-order phase transition, for positive values of 𝐷 𝐽 ⁄ 2𝑏 and for each film thickness N.