Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-05-03T23:21:33Z No. of bitstreams: 1 PriscilaValdeniaDosSantos_TESE.pdf: 1843795 bytes, checksum: 90c4e994c9a54d049c923beefec400bf (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-05-05T22:38:19Z (GMT) No. of bitstreams: 1 PriscilaValdeniaDosSantos_TESE.pdf: 1843795 bytes, checksum: 90c4e994c9a54d049c923beefec400bf (MD5) / Made available in DSpace on 2016-05-05T22:38:19Z (GMT). No. of bitstreams: 1 PriscilaValdeniaDosSantos_TESE.pdf: 1843795 bytes, checksum: 90c4e994c9a54d049c923beefec400bf (MD5) Previous issue date: 2015-07-15 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Neste trabalho investigamos o efeito dos campos aleat?rios no modelo Blume-Capel com intera??es de longo alcance. O modelo ? completamente sol?vel no ensemble can?nico, e sua densidade de energia livre nos leva a resultados correspondentes a uma teoria de campo m?dio. S?o estudados os casos para spin S = 1 sob influ?ncia de desordem temperada na presen?a de: (i) um campo cristalino aleat?rio; (ii) de um campo magn?tico aleat?rio; (iii) e de ambos. Para uma escolha adequada do campo aleat?rio, mostramos que o modelo apresenta uma variedade de comportamentos multicr?ticos, linhas de transi??o cont?nuas e de primeira ordem, al?m de fen?menos de re-entr?ncia. Os diagramas de fases, obtidos a partir do c?lculo da energia livre por spin, exibem diversas topologias em fun??o do par?metro que mede o grau de desordem. / In the presente work we investigate the ferromagnetic Blume-Capel (BC) model, for spin 1 and infinite-ranged interactions, under the influence of local quenched disorder. The model is exactly solved within the canonical ensemble. The obtained free energy density lead us to mean-field results. In the first part we study the BC model under the influence of a random crystal-field anisotropy, but otherwise without a magnetic field. In the second part we consider the BC model under a bimodal random magnetic field and a uniform crystal-field anisotropy term. This model was previously studied by Kaufman and Kanner. We give special attention to anisotropy versus temperature phase diagrams which may present reentrant phenomena. Finally, in the third part we consider a generalized version where both local fields - magnetic and crystal-field anisotropy - are diluted and, in the present case, modeled by discrete probability distribution. The phase diagram obtained and presented in this work exhibit a rich variety of multicritical behavior, presenting both continuous and first-order transition lines. Also, for some specific cases there is room for the existence of reentrant effects. This seems to be a characteristic of the Blume-Capel model under the presence of randomness.

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) 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 (eloihistoriador@yahoo.com.br) 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.