Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-01-23
Phys.Rev.B76:054408,2007
Physics
Condensed Matter
Disordered Systems and Neural Networks
v3: 9 pages, 10 figures, RevTex4, two figures added, discussion of graph ensembles and disorder averages expanded, estimate of
Scientific paper
10.1103/PhysRevB.76.054408
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 Neel 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.
Johnston Des
Weigel Martin
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