Bethe lattices in hyperbolic space
(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
- Söderberg, B. LU
- organization
- publishing date
- 1993
- 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
- 2021-01-03 04:02:41
@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}}, doi = {{10.1103/PhysRevE.47.4582}}, volume = {{47}}, year = {{1993}}, }