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Doctoral Thesis
DOI
10.11606/T.43.2017.tde-09082017-155024
Document
Author
Full name
Ricardo Paupitz Barbosa dos Santos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2002
Supervisor
Committee
Yokoi, Carlos Seihiti Orii (President)
Becerra, Carlos Castilla
Nobre, Fernando Dantas
Plascak, Joao Antonio
Salinas, Silvio Roberto de Azevedo
Title in Portuguese
Modelo de Ising diluído na rede de Bethe
Keywords in Portuguese
Magnetismo
Mecânica estatística
Mudança de fase
Abstract in Portuguese
Estudamos o modelo de Ising com diluição de sítios numa rede de Bethe. a estrutura hierárquica da rede de Bethe leva de forma natural às relações de recorrência satisfeitas pelas distribuições de probabilidade dos campos efetivos. As quantidades termodinâmicas na rede de Bethe são então expressas explicitamente em termos das distribuições limite dos campos efetivos. As distribuições dos campos efetivos em T=0 são obtidas de forma numericamente exata (isto é, se desprezarmos os erros de arrendodamento) e também analiticamente em alguns casos selecionados. Encontramos no caso de interações ferromagnéticas um número sempre finito de campos efetivos possíveis, mas no caso de interações antiferromagnéticas esse número pode divergir para valores irracionais do campo aplicado. Esses resultados fornecem o diagrama de fases campo aplicado versus concentração, numericamente exato, para antiferromagnetismo diluído em T=0. As distribuições dos campos efetivos são determinadas aproximadamente para T>0 e utilizadas para o cálculo de diferentes grandezas termodinâmicas. Apresentamos as curvas de magnetização, energia livre, energia interna e entropia. Esses cálculos fornecem o diagrama de fases aproximado no espaço tridimensional de campo aplicado, temperatura e concentração.
Title in English
Diluted Ising model on a Beth lattice
Keywords in English
Magnetism. Phase change
Statistical mechanics
Abstract in English
The site diluted Ising model is studied on a Beth lattice. The hierarchical structure of the Bethe lattice leads naturally to recursion relations obeyed by the probability distributions of the effective fields. The thermodynamic quantities on the Bethe lattice are then explicitly written in terms of the limiting distributions of the effective fields. Numerically exact results (i.e. if we neglect roundoff errors) for the distributions of the effective fields for T = 0 are presented, together with analytic results for select cases. It is found that the number of effective fields is always finite in the case of ferromagnetic interactions , but it might diverge for irrational values of the applied field in the case of antiferromagnetic interactions. These results yeld a numerically exact applied field versus concentration phase diagram for diluted antiferromagnet at T = 0. The distributions of the effective fields are computed aproximately for T > 0 and used to evaluete various thermodynamic quantities. Curves for the magnetization, free energy, internal energy and entropy are displayed. These calculations give an approximate three-dimensional phase diagram in the space of applied field, temperature and concentration.
 
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2002SantosBarbosa.pdf (1.17 Mbytes)
Publishing Date
2017-08-14
 
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