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Previous issue date: 2016-02-29 / Neste trabalho apresentamos solu??es para modelos de d?meros em redes planas mistas,
obtidas atrav?s do m?todo combinat?rio. Neste m?todo a fun??o de parti??o ? determinada
a partir da pfaffiana associada ao problema. Em particular foram determinadas, no
limite termodin?mico, as densidades de energia livre para redes 4-6, 3-6 e 3-4. Al?m da
densidade de energia livre para cada caso, calculamos tamb?m a liberdade molecular e a
densidade de entropia no limite de altas temperaturas. Foram tratados tr?s tipos diferentes
de redes 4-6, dois dos quais apresentam transi??es de fases. Mostramos tamb?m dois
tipos de redes 3-6 que possuem comportamentos cr?ticos parecidos com os casos das redes
4-6 discutidos neste trabalho. A rede 3-4 ? geometricamente semelhante ? rede triangular,
por?m apresentando comportamento cr?tico diferente. Em todos os casos, investigamos
numericamente o comportamento da densidade de energia livre e suas duas primeiras
derivadas, com a finalidade de compreender melhor o comportamento termodin?mico do
sistema. Revisamos tamb?m alguns resultados j? apresentados na literatura para as redes
quadrada, hexagonal, triangular e para a rede 4-8, usando a abordagem combinatorial
das pfaffianas. / In this study we present solutions for dimer models in mixed planar lattices, obtained from
combinatorial method. In this method the partition function is obtained from the pfaffian
associated with the problem. Particularly, in the thermodynamic limit, the free energy
densities for 4-6, 3-6 and 3-4 lattices were determined. Besides the determination of the
free energy for each case, we also computed the molecular freedom and the density of
entropy in the high temperature limit. We considered three types of distinct 4-6 lattices,
in which two of them exhibit phase transition. We also discuss the solutions for two types
of 3-6 lattices which exhibit critical behavior similar to the 4-6 lattices cases discussed in
the present work. The 3-4 lattice is geometrically similar to the triangular lattice problem,
but presents distinct critical behavior. In all cases, we study numerically the behavior
of free energy density as well as the behavior of its first derivatives, in order to better
understand the thermodynamic behavior of the corresponding system. We also revise
some results already presented in literature for the square, hexagonal, triangular and the
mixed 4-8 lattices, treated by the pfaffian combinatorial approach.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/23566 |
| Date | 29 February 2016 |
| Creators | Sousa, Ivandson Praeiro de |
| Contributors | 27023320482, http://lattes.cnpq.br/5307397723573993, Ara?jo, Jo?o Medeiros de, 32271026415, http://lattes.cnpq.br/3061734732654188, Queiroz J?nior, Idalmir de Souza, 63510731468, http://lattes.cnpq.br/8047604543096116, Costa, Francisco Alexandre da |
| Publisher | PROGRAMA DE P?S-GRADUA??O EM F?SICA, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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