Método variacional de Bogoliubov Aplicado a modelos de Spins: Ising e Blume-Capel

• Ano de defesa: 2017
• Autor(a) principal: Brito , Rejane Alves de
• Orientador(a): Plascak, João Antônio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba
• Programa de Pós-Graduação: Programa de Pós-Graduação em Física
• Departamento: Física
• País: Brasil
• Palavras-chave em Português: Modelo de Ising; Blume-Capel; desigualdade de Bogoliubov; campo médio; Ising Model; Bogoliubov inequality; mean eld
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9830

The spin-1=2 and spin-1 Ising models, as well as the spin-1 Blume-Capel model have been studied in one-, two-, and three-dimensional lattices. A variational method based on Bogoliubov inequality for the free-energy has been employed. The trial Hamiltonians consist of clusters of free spins, pairs of spins, and a combination of free spins and pairs of spins. For the three approximations, the thermodynamic quantities of interest have been calculated, together with the critical transition temperature and the behavior close to the transition, in the latter case in order to compute the corresponding critical exponents. The results have been compared to each other as well with exact results, when available, or results coming from more reliable approximate methods. It has been noted that as more interactions are taken into account in the trial Hamiltonian, better results are obtained for the transition temperature, although the critical exponents are always the mean eld like ones.