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Master's Dissertation
DOI
10.11606/D.54.1981.tde-20022014-175529
Document
Author
Full name
Fernando Dantas Nobre
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1981
Supervisor
Committee
Koberle, Roland (President)
Alcaraz, Francisco Castilho
Oliveira, Luiz Nunes de
Title in Portuguese
Teorias de calibre na rede com simetria z (n)
Keywords in Portuguese
Simetria Z (N)
Teoria Lattice Gauge
Abstract in Portuguese
Discutimos um modelo de calibre com simetria Z (N) na rede, sendo as variáveis dinâmicas definidas em faces de cubos. Mostramos a dualidade com um sistema de spins Z (N) em quatro dimensões e a autodualidade em seis dimensões para este modelo, utilizando o formalismo da matriz de transferência. Analisamos as funções de correlação invariantes por transformações de calibre, constatando os decaimentos exponenciais com o volume (para altas temperaturas e d ≥ 3) e com a área (para baixas temperaturas e d > 3). Para três dimensões, o modelo não apresenta transição de fase sendo exatamente solúvel. Estudamos também a versão U (1) do modelo e mostramos sua equivalência com uma teoria de campos clássica livre na região de baixas temperaturas
Title in English
Lattice gauge theories with Z(N) symmetry
Keywords in English
Lattice gauge theory
Z(N) symmetry
Abstract in English
We discussus a model with a Z (N) gauge symmetry on a lattice, the dynamical variables being defined on faces of cubes. The duality with a Z (N) spin system in four dimensions and the selfduality in six dimensions is shown for this model, using the transfer matrix formalism. The gauge invariant correlation functions have been analysed and we verify their exponential decay with volume (at high temperatures and d ≥ 3) and with the área (at low temperatures and d > 3). For three dimensions, the model exhibits no phase transition, being exactly soluble. We also study a U (I) version o four model and show its equivalence with a free classical field theory in the low temperature region
 
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Publishing Date
2014-02-21
 
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