Soft Modes, Localization and Two-Level Systems in Spin Glasses

TL;DR

This paper investigates the vibrational modes and energy landscape of three-dimensional Heisenberg spin glasses in a random field, revealing localized soft modes and potential two-level systems relevant for understanding glassy dynamics.

Contribution

It introduces a detailed analysis of inherent structures in spin glasses, identifying localized soft modes and their relation to two-level systems, advancing understanding of glassy behavior.

Findings

Density of states develops localized soft modes with $ ho()$ scaling as $$

A gap in the spectrum appears at large fields

Soft modes are linked to minima separated by small energy barriers

Abstract

In the three-dimensional Heisenberg spin glass in a random field we study the properties of the inherent structures that are obtained by an instantaneous cooling from infinite temperature. For not too large field the density of states $g(\omega)$ develops localized soft {\em plastic} modes and reaches zero as $\omega^4$ (for large fiels a gap appears). When we perturb the system adding a force along the softest mode one reaches very similar minima of the energy, separated by small barriers, that appear to be good candidates for classical two-level systems.