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Previous issue date: 2007-10-15 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / The ferromagnetic and antiferromagnetic Ising model on a two dimensional inhomogeneous lattice characterized by two exchange constants (J1 and J2) is investigated. The lattice allows, in a continuous manner, the interpolation between the uniforme square (J2 = 0) and triangular (J2 = J1) lattices. By performing Monte Carlo simulation using the sequential Metropolis algorithm, we calculate the magnetization and the magnetic susceptibility on lattices of differents sizes. Applying the finite size scaling method through a data colappse, we obtained the critical temperatures as well as the critical exponents of the model for several values of the parameter α = J2 J1 in the [0, 1] range. The ferromagnetic case shows a linear increasing behavior of the critical temperature Tc for increasing values of α. Inwhich concerns the antiferromagnetic system, we observe a linear (decreasing) behavior of Tc, only for small values of α; in the range [0.6, 1], where frustrations effects are more pronunciated, the critical temperature Tc decays more quickly, possibly in a non-linear way, to the limiting value Tc = 0, cor-responding to the homogeneous fully frustrated antiferromagnetic triangular case. / Investigamos o diagrama de fases do modelo de Ising, com intera??es feromagn?ticas e antiferromagn?ticas, emuma rede bidimensional inomog?nea caracterizada por duas constantes de troca (J1 e J2), a qual permite interpolar cont?nuamente as redes
quadrada (J2 = 0) e triangular (J2 = J1) uniformes. Utilizando o m?todo de simula??o de Monte Carlo, atrav?s da din?mica deMetropolis aplicada de forma seq?encial, calculamos a magnetiza??o e a susceptibilidade para redes de diversos tamanhos e aplicando t?cnicas de escalonamento para tamanhos finitos obtemos, atrav?s de um colapso de dados, valores para a temperatura cr?tica e expoentes cr?ticos em fun??o do par?metro α = J2 J1, contido no intervalo [0, 1]. No caso ferromagn?tico observamos que a temperatura cr?tica Tc cresce linearmente com α em todo o intervalo de varia??o deste par?metro, enquanto no caso antiferromagn?tico, o comportamento linear (decrescente) de Tc ? observado somente para pequenos valores de α; no intervalo [0.6, 1], onde os efeitos de frustra??o s?o mais pronunciados, a temperatura cr?tica sofre uma redu??o mais significativa, possivelmente n?o linear, para seu valor limite Tc = 0, que corresponde ? rede triangular homog?nea, antiferromagn?tica, completamente frustrada.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/16536 |
| Date | 15 October 2007 |
| Creators | Bezerril, Leonardo Mafra |
| Contributors | CPF:07136200482, http://lattes.cnpq.br/7218040405934056, Nobre, Fernando Dantas, CPF:13068164400, http://lattes.cnpq.br/2007917360087831, Souza, Adriano de Oliveira, CPF:38816687304, http://lattes.cnpq.br/5538200920343666, Mariz, Ananias Monteiro |
| Publisher | Universidade Federal do Rio Grande do Norte, Programa de P?s-Gradua??o em F?sica, UFRN, BR, F?sica da Mat?ria Condensada; Astrof?sica e Cosmologia; F?sica da Ionosfera |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| 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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