Study of the first-order phase transition in the classical and quantum random field Heisenberg model on a simple cubic lattice

Abstract

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 T * c (H), on the other hand in the continuous transition the magnetization is null at T = T c (H). At null temperature (T = 0) we have found the coexistence field H c = 3.23J that is independent of spin value. The transition temperature T c (H) for the classical case (S = ∞), in the T − H plane, is larger than the quantum case (S = 1/2).