Infinite Random Graphs as Statistical Mechanical Models

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Infinite Random Graphs as Statistical Mechanical Models. / Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria.

In: Acta Physica Polonica B, Vol. 4, No. 3, 2011, p. 287-304.

Research output: Contribution to journalJournal articleResearchpeer-review

Harvard

Durhuus, BJ & Napolitano, GM 2011, 'Infinite Random Graphs as Statistical Mechanical Models', Acta Physica Polonica B, vol. 4, no. 3, pp. 287-304. https://doi.org/10.5506/APhysPolBSupp.4.287

APA

Durhuus, B. J., & Napolitano, G. M. (2011). Infinite Random Graphs as Statistical Mechanical Models. Acta Physica Polonica B, 4(3), 287-304. https://doi.org/10.5506/APhysPolBSupp.4.287

Vancouver

Durhuus BJ, Napolitano GM. Infinite Random Graphs as Statistical Mechanical Models. Acta Physica Polonica B. 2011;4(3):287-304. https://doi.org/10.5506/APhysPolBSupp.4.287

Author

Durhuus, Bergfinnur Jøgvan ; Napolitano, George Maria. / Infinite Random Graphs as Statistical Mechanical Models. In: Acta Physica Polonica B. 2011 ; Vol. 4, No. 3. pp. 287-304.

Bibtex

@article{295cdeee3cf14766845316025d7d2385,
title = "Infinite Random Graphs as Statistical Mechanical Models",
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 influenced by the coupling to an Ising model in a constant magnetic field (B. Durhuus, G.M. Napolitano, in preparation)",
author = "Durhuus, {Bergfinnur J{\o}gvan} and Napolitano, {George Maria}",
year = "2011",
doi = "10.5506/APhysPolBSupp.4.287",
language = "English",
volume = "4",
pages = "287--304",
journal = "Acta Physica Polonica B",
issn = "0587-4254",
publisher = "Jagiellonian University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Infinite Random Graphs as Statistical Mechanical Models

AU - Durhuus, Bergfinnur Jøgvan

AU - Napolitano, George Maria

PY - 2011

Y1 - 2011

N2 - 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)

AB - 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)

U2 - 10.5506/APhysPolBSupp.4.287

DO - 10.5506/APhysPolBSupp.4.287

M3 - Journal article

VL - 4

SP - 287

EP - 304

JO - Acta Physica Polonica B

JF - Acta Physica Polonica B

SN - 0587-4254

IS - 3

ER -

ID: 33941670