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Doctoral Thesis
DOI
10.11606/T.43.1990.tde-27022014-120850
Document
Author
Full name
José Augusto Baeta Segundo
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1990
Supervisor
Committee
Perez, Jose Fernando (President)
Koberle, Roland
Oliveira, Paulo Murilo Castro de
Stilck, Jürgen Fritz
Wreszinski, Walter Felipe
Title in Portuguese
Sobre a Equivalência entre Ferromagnetos com Campos Aleatórios e Antiferromagnetos Diluídos
Keywords in Portuguese
Física
Mecânica estatística
Abstract in Portuguese
Usando um método proposto por van Hemmen nós computamos a energia livre da versão Curie-Weiss do modelo de Ising antiferromagnético com diluição de sítio na presença de um campo magnético uniforme. A solução apresenta uma correspondência exata entre as termodinâmicas deste modelo de Ising ferromagnético na presença de um campo magnético aleatório. Os diagramas de fase são discutidos e mostra-se a existência de um ponto tricrítico. Apresentamos também uma derivação alternativa dos resultados de van Hemmen a qual permite uma comparação com os métodos usuais de campo médio contidos na literatura. A solução obtida a partir da transformação de Hubbard-Stratorovich permite o cálculo das flutuações do parâmetro de ordem dos respectivos modelos e a constatação de uma equivalência também a este nível, em particular com a igualdade dos expoentes críticas relevantes.
Title in English
On the equivalence between ferromagnets with random fields and diluted antiferromagnetos.
Keywords in English
Physics
Statistical mechanics
Abstract in English
Using a method proposed by van Hemmen we compute the free energy of the Curie-Wiess version of the site-dilute antiferromagnetic Ising model in the presence of a uniform magnetic field. The solution displays an exact thermodynamic correspondence between this model and the Curie-Weiss version of the Ising model in the presence of a random magnetic field. The phase diagrams are discussed and a tricritical point is shown to exist. We present also an alternative derivation of van Hemmens results which allows an easy comparison with the usual mean-field methods used in the literature. The solution obtained via Hubbard-Stratorovich transformation allows the computation of the fluctuations of the order parameter in both models as to display their equivalence with equality of the relevant critical exponents.
 
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Publishing Date
2014-02-28
 
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