Universality in phase boundary slopes for spin glasses on self-dual lattices

Abstract

We study the effects of disorder on the slope of the disorder–temperature phase boundary near the Onsagerpoint (Tc = 2.269...) in spin-glass models. So far, studies have focused on marginal or irrelevant cases ofdisorder. Using duality arguments, as well as exact Pfaffian techniques, we reproduce theseanalytical estimates. In addition, we obtain different estimates for spin-glass models onhierarchical lattices where the effects of disorder are relevant. We show that the phaseboundary slope near the Onsager point can be used to probe for the relevance of disordereffects.