Random and frozen states in complex triangulations

Aste, Tomaso and Gramatica, Ruggero and Di Matteo, T. (2012) Random and frozen states in complex triangulations. Philosophical Magazine, 92 (1-3). pp. 246-254. ISSN 1478-6435. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Triangulations of complex surfaces with different genera are studied within a statistical mechanics framework where an energy is associated to deviations from an ideal, ordered ground state. We observe that the complexity of the embedding surface strongly affects the properties of the triangulations. At high temperatures the ‘random states’ have degree distributions that broaden with the surface genus. At low temperatures the ‘frozen states’ can reach a higher degree of order with increasing genus. The dynamics between disordered and ordered states is also affected by the surface genus. High genus triangulations start from more disordered states at high temperatures but they quench faster into more ordered states than the low genus counterparts. However, the ground state is never reached because at low temperatures the relaxation dynamics slows down into a glassy kind of behavior. Topological frustration can also play a very important role when the surface genus forces the average degree to be a fractional number.

Item Type: Article
Uncontrolled keywords: complex networks, triangulations, topological froths, surface genus, hyperbolic networks
Subjects: Q Science
Divisions: Faculties > Science Technology and Medical Studies > School of Physical Sciences > Functional Materials Group
Depositing User: Tomaso Aste
Date Deposited: 20 Mar 2012 15:58
Last Modified: 07 May 2014 10:31
Resource URI: https://kar.kent.ac.uk/id/eprint/29166 (The current URI for this page, for reference purposes)
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