A variational approach for the classical anisotropic Heisenberg model in a crystal field |
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| Authors: | DC CarvalhoLM Castro JA Plascak |
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| Institution: | a Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, C.P. 702, 30123-970 Belo Horizonte, MG, Brazilb Departamento de Ciências Exatas, Universidade Estadual do Sudoeste da Bahia, Estrada do Bem Querer Km04, CP 95, 45083-900 Vitoria da Conquista, BA, Brazilc Center for Simulational Physics, University of Georgia, Athens, GA 30602, USA |
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| Abstract: | The variational approach based on the Bogoliubov inequality for the free energy is used to study the three-dimensional anisotropic Heisenberg XXZ model with a crystal field. The magnetization and the phase diagrams are obtained as a function of the parameters of the Hamiltonian. Limiting cases, such as isotropic Heisenberg, XY, and planar rotator models in two and three dimensions, are analyzed and compared to previous results obtained from analytical approximations as well as to those obtained from more reliable approaches such as series expansion and Monte Carlo simulations. A parametric procedure has been used in order to simplify the solutions of the self-consistent coupled equations. |
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| Keywords: | Anisotropic Heisenberg model Variational approach Phase diagram |
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