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Doctoral Thesis
DOI
10.11606/T.43.1991.tde-16122013-141707
Document
Author
Full name
Pablo Serra
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1991
Supervisor
Committee
Stilck, Jürgen Fritz (President)
Alcaraz, Francisco Castilho
Chaves, Carlos Mauricio
Salinas, Silvio Roberto de Azevedo
Wreszinski, Walter Felipe
Title in Portuguese
Estudo de pontos tricríticos em modelos de polímeros sobre redes
Keywords in Portuguese
Fenômenos críticos
Mecânica estatística
Polímeros
Abstract in Portuguese
Estudamos vários modelos de polímeros (Caminhadas auto- e mutuamente excludentes sobre redes) que apresentam pontos tricríticos em seus diagramas de fases. Concentramos a nossa atenção nos problemas de polímeros com interações atrativas, nos quais o ponto tricrítico é conhecido como ponto H na literatura, e de polímeros na presença de diluição recozida. Analisamos o comportamento termodinâmico desses modelos na rede de Bethe e em gaxetas de Sierpinski bi- e tridimensionais, bem como na rede quadrada. Nas redes de Bethe e fractais foi possível obter soluções exatas. Já na rede quadrada empregamos métodos baseados na teoria de escala para sistemas finitos através do cálculo da matriz de transferência. Enfatizamos o estudo dos pontos tricríticos, dando particular atenção ao cálculo de seus expoentes nas redes fractais e quadrada. Na rede de Bethe, onde os expoentes são clássicos, foi possível estudar em detalhe o diagrama de fases do modelo com diluição e interações atrativas.
Title in English
Study of tricritical points on polymer model networks
Keywords in English
Critical phenomena
Polymers
Statistical mechanics
Abstract in English
We study several polymer models (self- and mutually avoiding walks on lattices) which display tricritical points in their phase diagrams. We concentrated our attention on the problems of polymers with attrative interactions, where the tricritical point is known as H point in the literature, and of polymers in the presence of annealed dilution. We considered the thermodynamic behavior of these models on the Bethe lattice, on the two- and three-dimentional Sierpinski gaskets, and on the square lattice. On the Bethe and the Sierpinski gaskets an exact solution could be obtained. On the square lattice we used finite size scaling methods together with transfer matrix calculations. We stressed the study of the tricritical points, paying particular attention to the calculation of their exponents on the fractal and the square lattice. On the Bethe lattice, where the exponents are classical, it was possible to study in detail the phase diagram of the model with dilution and attractive interactions.
 
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46018Serra.pdf (47.90 Mbytes)
Publishing Date
2014-02-21
 
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