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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2000.tde-20210729-205556
Document
Author
Full name
Fredy Walter Castellares Cáceres
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2000
Supervisor
Title in Portuguese
Modelo de Potts diluído
Keywords in Portuguese
Modelo De Potts
Processos Estocásticos
Abstract in Portuguese
O objetivo da dissertação é apresentar o modelo de aglomerados aleatórios e estudar sua relação com o modelo de Potts. Usando o modelo de aglomerados aleatórios, daremos condições necessárias e suficientes para a existência de magnetização espontânea nos modelos de Potts ferromagnético, homogêneo e diluído definido sobre a rede hipercúbica d-dimensional. Mostramos que existe quase certamente uma temperatura crítica determinística no modelo diluído, que é trivial (zero) se a probabilidade de não-diluição for menor ou igual à probabilidade crítica do modelo de percolação associado aos elos diluídos (perclação independente), e não trivial (positiva finita), caso contrário. Neste último caso, para temperaturas abaixoda crítica, mostramos que para quase toda realização da diluição, todo sítio que estiver num aglomerado infinito de elos não-diluidos está magnetizado
Title in English
not available
Abstract in English
The objective of this dissertation is to present the random cluster model and study its relation with the Potts model. using the random cluster model we give necessary and sufficient conditions for the existence of spontaneous magnetization inthe homogeneous and dilute ferromagnetic Potts model defined on the hypercubic d-dimensional lattice. We show that there almost surely exists a critical deterministic temperature in the dilute model, which is trivial (zero) if the probability ofnon-dilution is less than or equal to the critical probability of the percolation model associated to the dilute bonds (independent percolation), and non-trivial (positive almost surely and finite), in the opposite case. In the latter case, fortemperatures below critical, we show that almost surely site in an infinite cluster of non-dilute bonds is magnetized
 
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Publishing Date
2021-07-29
 
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