Modelos de d?meros em redes planares mistas

• Main Author: Sousa, Ivandson Praeiro de
• Other Authors: 27023320482
• Language: Portuguese
• Published: PROGRAMA DE P?S-GRADUA??O EM F?SICA 2017
• Subjects: CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA; D?meros; Modelos sol?veis; T?cnica das Pfaffianas; Resultados exatos; Transi??es de fases
• Online Access: https://repositorio.ufrn.br/jspui/handle/123456789/23566

Submitted by Automa??o e Estat?stica ([e-mail]) on 2017-07-03T14:11:15Z No. of bitstreams: 1 IvandsonPraeiroDeSousa_DISSERT.pdf: 2540138 bytes, checksum: 1275f137bef17f9cf08e9cd57ba5a24e (MD5) === Approved for entry into archive by Arlan Eloi Leite Silva ([e-mail]) on 2017-07-10T13:15:09Z (GMT) No. of bitstreams: 1 IvandsonPraeiroDeSousa_DISSERT.pdf: 2540138 bytes, checksum: 1275f137bef17f9cf08e9cd57ba5a24e (MD5) === Made available in DSpace on 2017-07-10T13:15:09Z (GMT). No. of bitstreams: 1 IvandsonPraeiroDeSousa_DISSERT.pdf: 2540138 bytes, checksum: 1275f137bef17f9cf08e9cd57ba5a24e (MD5) 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.