Análisis de Transiciones de Fase en un Ferromagneto idealaplicando el Método Monte Carlo a los Modelos de Ising y Heisenberg en 2 y 3 dimensiones

Abstract

Some results obtained from applying the Monte Carlo method to the models of Ising and Heisenberg for acrystal in 2 and 3 dimensions, where ferromagnetic phase transitions were detected, are presented. In particular,the Magnetization (|~M|) vs. Temperature (T) phase diagram is shown for 3 kinds of lattices (sc, bcc and fcc) for theHeisenberg 3D system in order to visualize the phase transition and calculate the respective critical temperatureTc.Then the values ofTcobtained for each of the analyzed systems (Ising 2D, Heisenberg 2D, Ising 3D y Heisenberg3D) are presented in a table, where we considered for each 3D case the cubic crystalline structrures mentioned.Taking into account that in a vicinity of the critical point (T≈Tc,H≈0) the main thermodynamic quantitiesobey universal scaling laws, the main critical exponentes (β,α,γ,δ) were calculated numerically for each systemfrom their respective phase diagrams, this permitted to verify the phenomenon of universality for each 3D system