Gibbs Measures for Models on Lines and Trees

• Ano de defesa: 2018
• Autor(a) principal: Endo, Eric Ossami
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Árvores de Cayley; Cayley trees; Dyson model; g-measures; g-medidas; Gibbs measures; Ising model; Medidas de Gibbs; Modelo de Dyson; Modelo de Ising
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-06052019-121811/

In this thesis we study various properties of the spins models, in particular, Ising and Dyson models. We study the stability of the phase transition of the nearest-neighbor ferromagnetic Ising model when we add a perturbation to the critical external field that becomes weaker far from the root of the Cayley tree. We also study the relation between g-measures and Gibbs measures, showing that the Dyson model at sufficiently low temperature is not a g-measure. Counting contours on trees is also studied, showing the characterization of the trees that have infinite number of contours, and comparisons between various definitions of contours. We also study the measures of the spatial Gibbs random graphs, and their local convergence.