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.287304 Abstract
 We discuss two examples of infinite random graphs obtained as limits
of finite statistical mechanical systems: a model of twodimensional discretized 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 socalled uniform infinite tree and results on the Hausdorff and spectral dimension of twodimensional spacetime 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 twodimensional discretized 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 socalled uniform infinite tree and results on the Hausdorff and spectral dimension of twodimensional spacetime 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:
http://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
 Jagellonian University, Cracow, Poland
 external identifiers

 scopus:84855969509
 ISSN
 05874254
 DOI
 10.5506/APhysPolBSupp.4.287
 language
 English
 LU publication?
 no
 id
 4e28eb5316584dfe96f4a2a2c46aa64f (old id 4123916)
 alternative location
 http://www.actaphys.uj.edu.pl/_old/sup4/pdf/s4p0287.pdf
 date added to LUP
 20131114 15:14:11
 date last changed
 20170101 05:58:47
@article{4e28eb5316584dfe96f4a2a2c46aa64f, abstract = {We discuss two examples of infinite random graphs obtained as limits<br/><br> of finite statistical mechanical systems: a model of twodimensional discretized 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 socalled uniform infinite tree and results on the Hausdorff and spectral dimension of twodimensional spacetime 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 = {05874254}, language = {eng}, number = {3}, pages = {287304}, 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}, }