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Physica A Statistical Mechanics and its Applications

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

J. Ricardo de Sousa, Douglas F. de Albuquerque, A.S. de Arruda

Published Feb 3, 2012• 10 citations
Publisher
DOI
10.1016/j.physa.2012.01.049

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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=\infty $ (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)Ψ(m)Ψ(m). Using Maxwell construction we have obtained the phase diagram in the T−HT-HT−H plane for all interval of field. The first-order transition temperature is calculated by the discontinuity of the magnetization at Tc∗(H)T_{c}^{\ast}(H)Tc∗​(H), on the other hand in the continuous transition the magnetization is null at T=Tc(H)T=T_{c}(H)T=Tc​(H). At null temperature (T=0) we have found the \textbf{coexistence} field Hc=3.23JH_{c}=3.23JHc​=3.23J that is independent of spin value. The transition temperature Tc(H)T_{c}(H)Tc​(H) for the classical case ($S=\infty $), in the T−HT-HT−H plane, is larger than the quantum case (S=1/2).
First- and second-order phase transitions in the isotropic Heisenberg model with multispin exchange were investigated with the help of the quantum Monte Carlo method. The calculations were performed for a system with spin S = 1/2 and N = L3 spins (L = 8, 12, and 16) on simple cubic lattices with periodic boundary conditions. A relation between the pair and multispin exchange constants for which the second- order phase transitions are replaced by first-order phase transitions is established. First-order phase transitions have not been studied previously by the quantum Monte Carlo method. Phase diagrams were constructed for the model under study. The computational results are compared with the method of Green’s functions and the molecular-field theory.