Modelo de Ginzburg-Landau a partir da teoria de campos a temperatura finita

• Autor(a) principal: Calza, Thiago Cheble Alves
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/12945
• topic: Thermal Field Theory; Matsubara Formalism; Spontaneous symmetry restoration; Ginzburg-Landau; Teoria de campos a temperatura finita; Transições de fase; Restauração de simetria. Modelo de Ginzburg-Landau; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DAS PARTICULAS ELEMENTARES E CAMPOS

In this work, we use the formalism of quantum field theories at finite temperature, as developed by Matsubara, applied to a Hamiltonian of N scalar fields with quartic self-interaction at N large. We get an expression in the first quantum approximation to the coeficient of the quadratic term of the Hamiltonian ("square mass"), renormalized as a function of temperature. From it, we study the process of spontaneous symmetry breaking. On the other hand, the same Hamiltonian is known as Ginzburg-Landau model in the literature of condensed matter, and allows the study of phase transitions in ferromagnetic materials. The temperature is introduced through the quadratic term in the Hamiltonian of the linear form: is proportional to the difference between the temperature and the critical temperature. This model, however, is valid only in the region of temperatures close to criticality. As a result of our calculations in the field theory at finite temperature, we observed that in a range of values around the critical temperature, the quadratic mass can be approximated by a linear relation with the temperature. This highlights the compatibility of the Ginzburg-Landau approach, in the vicinity of criticality with respect to the formalism of finite temperature field. We also discuss the effects caused by the presence of a chemical potential in the system.