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Infinite Random Graphs as Statistical Mechanical Models

Durhuus, Bergfinnur and Napolitano, George LU (2011) In Acta Physica Polonica. Series B: Elementary Particle Physics, Nuclear Physics, Statistical Physics, Theory of Relativity, Field Theory 4(3). p.287-304
Abstract
We discuss two examples of infinite random graphs obtained as limits

of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a relation to the so-called uniform infinite tree and results on the Hausdorff and spectral dimension of two-dimensional space-time obtained in B. Durhuus, T. Jonsson, J.F. Wheater, J. Stat. Phys. 139, 859 (2010) are briefly outlined. For the latter we discuss results on the absence of spontaneous magnetization and argue that, in the generic case, the values of the Hausdorff and spectral dimension of the underlying infinite trees are not... (More)
We discuss two examples of infinite random graphs obtained as limits

of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a relation to the so-called uniform infinite tree and results on the Hausdorff and spectral dimension of two-dimensional space-time obtained in B. Durhuus, T. Jonsson, J.F. Wheater, J. Stat. Phys. 139, 859 (2010) are briefly outlined. For the latter we discuss results on the absence of spontaneous magnetization and argue that, in the generic case, the values of the Hausdorff and spectral dimension of the underlying infinite trees are not influenced by the coupling to an Ising model in a constant magnetic field (B. Durhuus, G.M. Napolitano, in preparation) (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
in
Acta Physica Polonica. Series B: Elementary Particle Physics, Nuclear Physics, Statistical Physics, Theory of Relativity, Field Theory
volume
4
issue
3
pages
287 - 304
publisher
Jagellonian University, Cracow, Poland
external identifiers
  • scopus:84855969509
ISSN
0587-4254
DOI
10.5506/APhysPolBSupp.4.287
language
English
LU publication?
no
id
4e28eb53-1658-4dfe-96f4-a2a2c46aa64f (old id 4123916)
alternative location
http://www.actaphys.uj.edu.pl/_old/sup4/pdf/s4p0287.pdf
date added to LUP
2013-11-14 15:14:11
date last changed
2017-01-01 05:58:47
@article{4e28eb53-1658-4dfe-96f4-a2a2c46aa64f,
  abstract     = {We discuss two examples of infinite random graphs obtained as limits<br/><br>
of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a relation to the so-called uniform infinite tree and results on the Hausdorff and spectral dimension of two-dimensional space-time obtained in B. Durhuus, T. Jonsson, J.F. Wheater, J. Stat. Phys. 139, 859 (2010) are briefly outlined. For the latter we discuss results on the absence of spontaneous magnetization and argue that, in the generic case, the values of the Hausdorff and spectral dimension of the underlying infinite trees are not influenced by the coupling to an Ising model in a constant magnetic field (B. Durhuus, G.M. Napolitano, in preparation)},
  author       = {Durhuus, Bergfinnur and Napolitano, George},
  issn         = {0587-4254},
  language     = {eng},
  number       = {3},
  pages        = {287--304},
  publisher    = {Jagellonian University, Cracow, Poland},
  series       = {Acta Physica Polonica. Series B: Elementary Particle Physics, Nuclear Physics, Statistical Physics, Theory of Relativity, Field Theory},
  title        = {Infinite Random Graphs as Statistical Mechanical Models},
  url          = {http://dx.doi.org/10.5506/APhysPolBSupp.4.287},
  volume       = {4},
  year         = {2011},
}