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  Properties of Quantum Graphity at Low Temperature

Caravelli, F., & Markopoulou, F. (2011). Properties of Quantum Graphity at Low Temperature. Physical Review D, 84(2): 024002. doi:10.1103/PhysRevD.84.024002.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-0705-8 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-0706-6
Genre: Journal Article

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 Creators:
Caravelli, Francesco, Author
Markopoulou, Fotini1, Author              
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
 Abstract: We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use this method to study the properties of Quantum Graphity models at low temperature in the limit in which the valence coupling constant of the model is much greater than the coupling constants of the loop terms. Using mean field theory we find that an order parameter for the model is the average valence of the graph. We calculate the equilibrium distribution for the valence as an implicit function of the temperature. In the approximation in which the temperature is low, we find the first two Taylor coefficients of the valence in the temperature expansion. A discussion of the susceptibility function and a generalization of the model are given in the end.

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 Dates: 2010-08-072011-05-122011
 Publication Status: Published in print
 Pages: 21 pages, 5 figures; a plot added, corrections added; Accepted for publication in PRD
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1008.1340
DOI: 10.1103/PhysRevD.84.024002
URI: http://arxiv.org/abs/1008.1340
 Degree: -

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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : Published for the American Physical Society by the American Institute of Physics
Pages: - Volume / Issue: 84 (2) Sequence Number: 024002 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258