Spin lattice systems at low temperature

• Ano de defesa: 2024
• Autor(a) principal: Souza, Kelvyn Emmanoel de Castro Martins Welsch de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Cluster expansion; Expansão em polímeros; Hubbard; Long-range; Longo-alcance; Mecânica estatística quântica; Pirogov-Sinai; Quantum statistical mechanics
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-26022024-174722/

In this work, two main aspects of low-temperature spin systems are considered --- the cluster expansion for long-range Ising-type models and the construction of the phase diagram when quantum perturbations are present. With respect to the first subject, we present a new result stating that the cluster expansion does converge for interactions with polynomial decay \\alpha, for any \\alpha > d \\geq 2, provided that the contours are defined in a suitable manner. As for the second subject, we review a paper due to Borgs, Kotecký and Ueltschi, which extends Pirogov-Sinai theory and whose main result is that, even with quantum perturbations, the low-temperature phase diagram is homeomorphic to the zero-temperature one.