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Spin lattice systems at low temperature

Souza, Kelvyn Emmanoel De Castro Martins Welsch De

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Título:
Spin lattice systems at low temperature
Autor: Souza, Kelvyn Emmanoel De Castro Martins Welsch De
Orientador: Proença, Rodrigo Bissacot
Assuntos: Expansão Em Polímeros; Hubbard; Longo-Alcance; Mecânica Estatística Quântica; Pirogov-Sinai; Cluster Expansion; Long-Range; Quantum Statistical Mechanics
Notas: Dissertação (Mestrado)
Descrição: 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.
DOI: 10.11606/D.45.2024.tde-26022024-174722
Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Matemática e Estatística
Data de criação/publicação: 2024-02-06
Formato: Adobe PDF
Idioma: Inglês

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