Frustration effects in antiferromagnets on planar random graphs

TL;DR

This paper investigates how geometric frustration in random planar graphs affects antiferromagnetic models, revealing that frustration can eliminate finite-temperature transitions and induce spin-glass phases, contrasting with ferromagnetic behavior.

Contribution

It introduces the study of frustration effects in antiferromagnets on random planar graphs, highlighting differences between annealed and quenched disorder and their impact on magnetic phases.

Findings

Finite-temperature transitions are suppressed in some antiferromagnetic models due to frustration.

Annealed graphs can support Neel order, while quenched graphs lead to spin-glass phases.

Frustration effects differ markedly between ferromagnetic and antiferromagnetic models on random graphs.

Abstract

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.