• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Doctoral Thesis
DOI
10.11606/T.43.1983.tde-17122013-153220
Document
Author
Full name
Jürgen Fritz Stilck
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1983
Supervisor
Committee
Salinas, Silvio Roberto de Azevedo (President)
Oliveira, Mario Jose de
Qualifik, Paul
Title in Portuguese
Estudos relacionados com o modelo de 12 vértices para a transição de fases antiferroelétrica do ácido quadrático
Keywords in Portuguese
Baixa temperatura
Abstract in Portuguese
São propostos modelos de 4 e de 12 vértices na rede quadrada para explicar a transição de fases antiferroelétrica observada no ácido quadrático (H IND. 2C IND. 4O IND. 4). A energia livre do modelo básico de 4 vértices se anula identicamente. A solução do modelo iônico de 12 vértices na aproximação de Bethe apresenta uma transição de segunda ordem. A existência desta transição de fases é assegurada por meio de um argumento de Peierls . A transição de fases do modelo de 12 vértices também é estudada pela técnica do grupo de renormalização fenomenológico. Conclui-se que a temperatura critica exata deve ser sistematicamente inferior àquela prevista pela aproximação de Bethe. Há evidências de que nü = 1. A mesma técnica foi empregada no estudo de um modelo de 16 vértices equivalente ao modelo de Ising, reproduzindo- se com boa precisão os cálculos exatos. Resultados experimentais mais recentes para O ácido quadrático indicam urna transição de primeira ordem. Mostra- se então que um modelo compressível de 12 vértices apresenta urna transição descontinua na aproximação de Bethe.
Title in English
Studies related to the model of 12 vertices for the antiferroelectric phase transition of
Keywords in English
Low temperature
Abstract in English
We consider 4 and 12 vertex models on the square lattice for the antiferroelectric phase transition in crystals of squaric acid (H IND. 2C IND. 4O IND. 4). The free energy of the basic 4 vertex model vanishes identically. In the framework of the Bethe approximation, the ionic 12 vertex model gives a second order phase transition. We use a Peierls argument to show that a phase transition does indeed occur in this model. Also, the phase transition in the 12 vertex model is studied by means of phenomenological renormalization group calculations. The exact critical temperature seems to be always lower than the prediction of the Bethe approximation. We present evidences that nü = 1 for this model. The same calculations were done for a 16 vertex model which is equivalent to the Ising model, the exact results being reproduced with good precision. Recent experimental data seem to support that the transition in squaric acid is indeed of first order. A compressible 12 vertex model is then shown to give a discontinuous transition.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
46059FritzStilck.pdf (68.34 Mbytes)
Publishing Date
2014-02-20
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2022. All rights reserved.