2011/10/20 by Ricardo de Sousa, Douglas F. de Albuquerque, de Sousa, Ricardo +4
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1110.4666
10 pages, 1 figure
openalex publication_date 2011/10/20 · arxiv created 2011/10/21 · arxiv updated 2011/10/24 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28
The phase diagram of the Heisenberg ferromagnetic model in the presence of a magnetic random field (we have used bimodal distribution) of spin S=1/2 (quantum case) and S=∞ (classical case) on a simple cubic lattice is studied within the framework of the effective-field theory in finite cluster (we have chosen N=2 spins). Integrating out the part of order parameter (equation of state), we obtained an effective Landau expansion for the free energy written in terms of the order parameter Ψ(m). Using Maxwell construction we have obtained the phase diagram in the T-H plane for all interval of field. The first-order transition temperature is calculated by the discontinuity of the magnetization at Tc∗(H), on the other hand in the continuous transition the magnetization is null at T=Tc(H). At null temperature (T=0) we have found the coexistence field Hc=3.23J that is independent of spin value. The transition temperature Tc(H) for the classical case (S=∞ ), in the T-H plane, is larger than the quantum case (S=1/2).