Made available in DSpace on 2014-12-17T15:14:46Z (GMT). No. of bitstreams: 1 AntonioSAF.pdf: 1214999 bytes, checksum: c500092609bb7d7681af9a0f37dcaf88 (MD5) Previous issue date: 2008-11-14 / High-precision calculations of the correlation functions and order parameters were performed in order to investigate the critical properties of several two-dimensional ferro- magnetic systems: (i) the q-state Potts model; (ii) the Ashkin-Teller isotropic model; (iii) the spin-1 Ising model. We deduced exact relations connecting specific damages (the difference between two microscopic configurations of a model) and the above mentioned thermodynamic quanti- ties which permit its numerical calculation, by computer simulation and using any ergodic dynamics. The results obtained (critical temperature and exponents) reproduced all the known values, with an agreement up to several significant figures; of particular relevance were the estimates along the Baxter critical line (Ashkin-Teller model) where the exponents have a continuous variation. We also showed that this approach is less sensitive to the finite-size effects than the standard Monte-Carlo method. This analysis shows that the present approach produces equal or more accurate results, as compared to the usual Monte Carlo simulation, and can be useful to investigate these models in circumstances for which their behavior is not yet fully understood / Atrav?s de c?lculos de alta precis?o das fun??es de correla??o e dos par?metros de ordem, investigamos as propriedades cr?ticas de v?rios modelos ferromagn?ticos bidimensionais, a saber: (i) Potts q-estados; (ii) Ashkin-Teller isotr?pico; (iii) Ising de spin-1. Utilizamos simula??es computacionais, obtidas a partir de rela??es anal?ticas exatas, conectando as quantidades acima mencionadas e certas combina??es de Danos (diferen?as entre duas configura??es microsc?picas de um modelo), que s?o v?lidas para qualquer din?mica erg?dica. Todos os resultados encontrados (temperaturas e expoentes cr?ticos) concordam com os valores conhecidos, em v?rias casas decimais, destacando-se em particular a reprodu??o da linha de Baxter (no caso ii) onde os expoentes variam continuamente, resultado de dif?cil obten??o por m?todos tradicionais. Tamb?m mostramos que este m?todo ? menos sens?vel aos efeitos de tamanho finito que aqueles baseados no procedimento usual de simula??o de Monte-Carlo. Tais fatos indicam a potencialidade desta abordagem para investigar situa??es ainda insuficientemente exploradas, nos modelos acima analisados e em outros semelhantes

Made available in DSpace on 2014-12-17T15:14:47Z (GMT). No. of bitstreams: 1 DarlanAM.pdf: 1159480 bytes, checksum: d201bf0e3558be6b14b14c9a86a46f20 (MD5) Previous issue date: 2005-03-10 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / In this work we have studied the problem of percolation in a multifractal geometric support, in its different versions, and we have analysed the conection between this problem and the standard percolation and also the connection with the critical phenomena formalism. The projection of the multifractal structure into the subjacent regular lattice allows to map the problem of random percolation in the multifractal lattice into the problem of correlated percolation in the regular lattice. Also we have investigated the critical behavior of the invasion percolation model in this type of environment. We have discussed get the finite size effects / Nesta disserta??o estudamos o problema da percola??o num suporte geom?trico multifractal, em suas diferentes vers?es, e analisamos a conex?o deste problema com a percola??o convencional e com o formalismo dos fen?menos cr?ticos. A proje??o da estrutura multifractal numa rede regular subjacente permite mapear o problema da percola??o aleat?ria no multifractal num problema de percola??o correlacionada numa rede regular. Tamb?m investigamos o comportamento cr?tico do modelo da percola??o por invas?o neste tipo de ambiente e discutimos a quest?o do efeito de tamanho finito

Made available in DSpace on 2014-12-17T15:14:59Z (GMT). No. of bitstreams: 1 ClaudionorGB_DISSERT.pdf: 2304268 bytes, checksum: 610cbceb61cd582290dc8b795fa3a210 (MD5) Previous issue date: 1994-05-24 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Estudamos as propriedades cr?ticas (diagrama de fases e classes de universalidade) do modelo de Ashkin-Teller anisotr?pico ferromagn?tico, cujo hamiltoniano ? dado por: H = -&#8721;_(<ij>)&#9618;&#12310;{J1TiTj+J2&#963;i&#963;j+J4&#963;i&#963;jTiTj}&#12311; com: J1 + J2 &#8805; 0, J1 + J4 &#8805; 0 , J2 + J4 &#8805; 0, ( &#963;, r = ? 1 ). Utilizamos o m?todo do Grupo de Renormaliza??o no espa?o real, aplicado a uma rede hier?rquica que serve como aproxima??o para a rede quadrada. Observamos a exist?ncia de 5 fases : (i) Paramagn?tica ( P : < &#963; > =< &#428; > =< &#963;&#428; >= 0) ; (ii) Intermedi?ria ( I : < &#963; > =< &#428; >= 0, < &#963;&#428; > &#8800; 0) ; (iii) Ferromagn?tica ( F : < &#963; > &#8800; 0, < &#428; > &#8800; 0, < &#963;&#428; > &#8800; 0) ; (iv) Ferro &#963; ( F&#963; : < &#963; > &#8800; 0, < &#428; >=< &#963;&#428; >= 0 ) ; (v) Ferro &#963; ( F&#428; : < &#428; > &#8800; 0, < &#963; >=< &#963;&#428; >= 0 ). As fronteiras cr?ticas obtidas reproduzem todos os valores exatos conhecidos (em pontos especiais) para a rede quadrada