Recobrimentos no espaço hiperbólico e percolação na árvore binária estendida

We study the percolation problem on the enhanced binary tree, a simple structure that exhibits geometric features of hyperbolic spaces: a non-vanishing surface-volume ratio, the latter being compact. The violation of Euclid s fifth postulate, assuring the possibility of an infinity of paralel to a given ray meeting at a point, allows for a richer set of phenomena, like the existence of infinite giant clusters coexisting on a critical phase. We find two phase transitions for this tree, as reported on the literature, the first being on the universality class as percolation on hyperbolic lattices. Our results for the second phase transition agree with some results from the literature, although better studies are needed in order to assess its true scaling behavior.

Grantor

Programa de Pós-graduação em Física

Year dc:date.issued

2011

Author dc:creator

• Lara, Vitor de Oliveira Moraes

• Mecânica estatística
• Geometria hiperbólica
• Geometria euclidiana
• Transição de fase
• Fenômeno crítico

Statement dc:rights

• Acesso Aberto

Language dc:language

por

Repository record dc:identifier.uri

https://app.uff.br/riuff/handle/1/19239

OAI identifier oai:identifier

oai:app.uff.br:1/19239