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

TL;DR

This paper investigates how disorder influences the slope of the phase boundary in spin-glass models near the critical temperature, revealing universal behaviors and the relevance of disorder effects using duality and exact techniques.

Contribution

It introduces a novel approach to analyze the relevance of disorder effects on phase boundary slopes in spin glasses using duality and exact Pfaffian methods.

Findings

Universal phase boundary slopes near the Onsager point.

Different estimates for models on hierarchical lattices.

Phase-boundary slope as a probe for disorder relevance.

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.