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Bethe lattices in hyperbolic space

Söderberg, B. LU (1993) In Physical Review E 47(6). p.4582-4584
Abstract

A recently suggested geometrical embedding of Bethe-type lattices (branched polymers) in the hyperbolic plane [R. Mosseri and J. F. Sadoc, J. Phys. Lett. 43, L249 (1982); J. A. de Miranda-Neto and F. Moraes, J. Phys. I. France 2, 1657 (1992)] is shown to be only a special case of a whole continuum of possible realizations that preserve some of the symmetries of the Bethe lattice. The properties of such embeddings are investigated and relations to Farey trees, devil's staircases, and Apollonian tiling are pointed out.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E
volume
47
issue
6
pages
3 pages
publisher
American Physical Society
external identifiers
  • scopus:0342415811
ISSN
1063-651X
DOI
10.1103/PhysRevE.47.4582
language
English
LU publication?
yes
id
d39ed8ca-2e72-4fd7-99cc-8a079820f20e
date added to LUP
2016-10-03 19:22:40
date last changed
2017-01-03 10:20:53
@article{d39ed8ca-2e72-4fd7-99cc-8a079820f20e,
  abstract     = {<p>A recently suggested geometrical embedding of Bethe-type lattices (branched polymers) in the hyperbolic plane [R. Mosseri and J. F. Sadoc, J. Phys. Lett. 43, L249 (1982); J. A. de Miranda-Neto and F. Moraes, J. Phys. I. France 2, 1657 (1992)] is shown to be only a special case of a whole continuum of possible realizations that preserve some of the symmetries of the Bethe lattice. The properties of such embeddings are investigated and relations to Farey trees, devil's staircases, and Apollonian tiling are pointed out.</p>},
  author       = {Söderberg, B.},
  issn         = {1063-651X},
  language     = {eng},
  number       = {6},
  pages        = {4582--4584},
  publisher    = {American Physical Society},
  series       = {Physical Review E},
  title        = {Bethe lattices in hyperbolic space},
  url          = {http://dx.doi.org/10.1103/PhysRevE.47.4582},
  volume       = {47},
  year         = {1993},
}