RECOBRIMENTOS NO ESPAÇO HIPERBÓLICO E PERCOLAÇÃO NA ÁRVORE BINÁRIA ESTENDIDA
Geometria hiperbólica
Geometria euclidiana
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CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA
Abstract
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.
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Subject(s)
Mecânica estatísticaGeometria hiperbólica
Geometria euclidiana
Transição de fase
Fenômeno crítico
CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA