Infinite Random Graphs as Statistical Mechanical Models
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4123916
- author
- Durhuus, Bergfinnur and Napolitano, George LU
- publishing date
- 2011
- 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
- Jagiellonian 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
- 2016-04-01 13:57:53
- date last changed
- 2022-01-27 22:06:00
@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 = {{Jagiellonian 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}}, doi = {{10.5506/APhysPolBSupp.4.287}}, volume = {{4}}, year = {{2011}}, }