Delocalization transition in low energy excitation modes of vector spin glasses – Archive ouverte HAL

Silvio Franz ¹ Flavio Nicoletti ^{1, 2} Giorgio Parisi ² Federico Ricci-Tersenghi ²

Silvio Franz, Flavio Nicoletti, Giorgio Parisi, Federico Ricci-Tersenghi. Delocalization transition in low energy excitation modes of vector spin glasses. SciPost Physics, SciPost Foundation, 2022, 12 (1), pp.016. ⟨10.21468/SciPostPhys.12.1.016⟩. ⟨hal-03738539⟩

We study the energy minima of the fully-connected m m -components vector spin glass model at zero temperature in an external magnetic field for m\ge 3 m ≥ 3 . The model has a zero temperature transition from a paramagnetic phase at high field to a spin glass phase at low field. We study the eigenvalues and eigenvectors of the Hessian in the minima of the Hamiltonian. The spectrum is gapless both in the paramagnetic and in the spin glass phase, with a pseudo-gap behaving as \lambda^{m-1} λ m − 1 in the paramagnetic phase and as \sqrt{\lambda} λ at criticality and in the spin glass phase. Despite the long-range nature of the model, the eigenstates close to the edge of the spectrum display quasi-localization properties. We show that the paramagnetic to spin glass transition corresponds to delocalization of the edge eigenvectors. We solve the model by the cavity method in the thermodynamic limit. We also perform numerical minimization of the Hamiltonian for N\le 2048 N ≤ 2048 and compute the spectral properties, that show very strong corrections to the asymptotic scaling approaching the critical point.

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. Department of Physics [Roma La Sapienza]