publication . Doctoral thesis . 2018

Gibbs Measures for Models on Lines and Trees

Eric Ossami Endo;
Open Access English
  • Published: 31 Jul 2018
  • Publisher: BR
Abstract
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 measure...
Subjects
free text keywords: Árvores de Cayley, g-medidas, Medidas de Gibbs, Modelo de Dyson, Modelo de Ising, Cayley trees, Dyson model, g-measures, Gibbs measures, Ising model
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