Estudo analítico de modelos tipo XY tridimensionais puros e diluídos via Princípio Variacional de Bogoliubov

Detalhes bibliográficos
Ano de defesa: 2015
Autor(a) principal: Diego da Cunha Carvalho
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Minas Gerais
UFMG
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://hdl.handle.net/1843/BUOS-8GALUX
Resumo: In this work, we have analytically studied, by means of the Bogoliubov Variational Principle (BVP), the pure Heisenberg and XY with bond dilution models, both ferromagnetic, classical (continuous spins), anisotropic, three-dimensional and in the presence of a crystalline field. Furthermore, we have shown the equivalence between the BVP and theSelf-Consistent Harmonic Approximation (SCHA) a trial harmonic Hamiltonian. In the study of anisotropic Heisenberg model, the magnetization and phase diagrams are obtained as a function of parameters of the Hamiltonian. Limiting cases, such as the isotropicHeisenberg, XY and Planar Rotor models in two and three dimensions are analyzed and compared to previous results obtained from analytical approximations and Monte Carlo simulations. In the study of anisotropic XY model with bond dilution, we have obtained the critical concentration and compared with the exact result as well as from other approximation methods, besides reviewing the Planar Rotor diluted system as a limitingcase. By showing the equivalence between the BVP and SCHA, we arrive at a system of coupled equations for the variational parameters, which arise by employing the BVP, and the system of coupled equations for the coupling constants that appear employing the SCHA, and we found that such systems are identical.