Study of the first-order phase transition in the classical and quantum random field Heisenberg model on a simple cubic lattice
| Autor: | de Sousa, Ricardo, de Albuquerque, Douglas F., Arruda, Alberto S. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Psi (m)$. 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 $T_{c}^{\ast}(H)$, 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 \textbf{coexistence} field $H_{c}=3.23J$ that is independent of spin value. The transition temperature $T_{c}(H)$ for the classical case ($S=\infty $), in the $T-H$ plane, is larger than the quantum case (S=1/2). Comment: 10 pages, 1 figure |
| Databáze: | arXiv |
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