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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 Johnston2 — 1Institut 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.