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Master's Dissertation
DOI
10.11606/D.54.1988.tde-30042009-101638
Document
Author
Full name
Francisco de Assis Ribas Bosco
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1988
Supervisor
Committee
Rosa Junior, Sylvio Goulart (President)
Alcaraz, Francisco Castilho
Alfonso, Nestor Felipe Caticha
Title in Portuguese
Propriedades geométricas do grupo de renormalização em redes hierárquicas.
Keywords in Portuguese
Grupo de renormalização no espaço real
Modelo de Potts
Redes hierárquicas
Abstract in Portuguese
Neste trabalho estudamos o comportamento crítico do modelo de Potts p-estados na árvore de Cayley, através das propriedades do conjunto de zeros de Yang-Lee da função de partição. Tratando a transformação do grupo de renormalização como um mapeamento racional na esfera de Riemann utiliza-se alguns resultados da teoria de Julia e Fatou para obter-se uma descrição geométrica do comportamento crítico do modelo. Mostra-se de que forma o conjunto de zeros de Yang-Lee se relaciona com o conjunto de Julia do mapa do grupo de renormalização, e calculam-se alguns parâmetros geométricos desse conjunto que descrevem o comportamento não universal do modelo.
Title in English
Geometrical properties of the renormalization group in hierarchical lattices.
Keywords in English
Hierarchical lattices
Potts Model
Real space renormalization group
Abstract in English
We study the critical behavior of the p-state Potts model on a Cayley tree, looking for the properties of the Yang-Lee zeros set of the partition function. We treated the renormalization group transformation as a rational mapping on the Riemann sphere, and use some results from the Julia and Fatou theory to obtain a geometrical description of the critical properties of the model. We show how the Yang-Lee zeros set is associated with the Julia set of the renormalization group map, and we also calculate some geometrical parameters of this set which describes the non-universal behavior of the model.
 
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Publishing Date
2009-05-15
 
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