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

8 pages, 6 figures

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• Duality analysis on random planar lattice
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Stability of topologically-protected quantum computing proposals as seen through spin glasses
• An extension of estimation of critical points in ground state for random spin systems