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

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 $g(ω)$ develops localized soft {\em plastic} modes and reaches zero as $ω^4$ (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.