Simulação de modelos na classe KPZ em 3 e 4 dimensões

• Autor(a) principal: Euzébio, Jônatas Araujo Ribeiro
• Data de Publicação: 2009
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal Fluminense (RIUFF)
• Texto Completo: https://app.uff.br/riuff/handle/1/18629
• topic: Cristal; Superfície; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA

We studied two questions that are still unclear concerning the interfaces growth equation of Kardar, Parisi and Zhang (KPZ): the existence or not of a superior critical dimension, and the universality of the height distributions at the steady state. There are controversies among previous works related to the existence of a finite value for the superior critical dimension (dc) for the KPZ equation. While some of them point to the value dc = 4, others indicate dc = 1. By simulations of KPZ discret growth models (etching and RSOS) we show that, if it exists, dc > 4. As we will see later, if we assumed that dc is equal to 4, we should obtain the scaling exponents Æ = 0 and z = 2 in that dimension, and a logarithmic scaling relation between the interface width at the saturation regime and the linear size of the substrate should be observed. However, besides excluding this logarithmic relation, our data lead us to 0:185 < Æ < 0:25 and z < 2 for the roughness and the dynamic exponents respectively, discarding dc = 4. In dimension d = 3, our estimates suggest Æ º 0:3 and z º 1:7. Moreover, we point in favor of the universality of height distributions of different KPZ discret growth models, by calculating the skewness S and the kurtosis Q for the mentioned models in dimensions d = 3 and d = 4. In d = 3, we have j S j= 0:39ß0:02 and 0:25 · Q · 0:3, while in d = 4 we have j S j= 0:45 ß 0:03 and Q º 0:4.