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Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Statistical physics of complex networks II

DY 22.6: Talk

Wednesday, February 27, 2008, 18:00–18:15, MA 004

Frustration from Fat Graphs — •Martin Weigel1 and Des Johnston21Institut für Physik, KOMET 331, Johannes-Gutenberg-Universität* Mainz, Staudinger Weg 7, 55099 Mainz, Germany — 2Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK

We consider the effect of geometric frustration induced by the random distribution of loop lengths in the “fat” graphs of the dynamical triangulations model on coupled antiferromagnets. While the influence of such connectivity disorder is rather mild for ferromagnets in that an ordered phase persists and only the properties of the phase transition are substantially changed in some cases, any finite-temperature transition is wiped out due to frustration for some of the antiferromagnetic models. A wealth of different phenomena is observed: while for the annealed average of quantum gravity some graphs can adapt dynamically to allow the emergence of a Néel ordered phase, this is not possible for the quenched average, where a zero-temperature spin-glass phase appears instead. We relate the latter to the behaviour of conventional spin-glass models coupled to random graphs.
[1] M. Weigel and D. Johnston, Phys. Rev. B 76 (2007) 054408.

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