Delocalization transition in low energy excitation modes of vector spin glasses

Abstract

We study the energy minima of the fully-connected $m$-components vector spin glass model at zero temperature in an external magnetic field for $m\ge 3$. 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 ${\lambda }^{m-1}$ in the paramagnetic phase and as $\sqrt{\lambda }$ 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 $N\le 2048$ and compute the spectral properties, that show very strong corrections to the asymptotic scaling approaching the critical point.

References in corpus (30)

• Spin-Glass Theory for Pedestrians
• Vibrational modes identify soft spots in a sheared disordered packing
• Anharmonicity, vibrational instability and Boson peak in glasses
• Continuum limit of the vibrational properties of amorphous solids
• Statistics and properties of low-frequency vibrational modes in structural glasses
• Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution
• Low-frequency vibrational modes of stable glasses
• Bosonic Excitations in Random Media
• Universal non-phononic density of states in 2D, 3D and 4D glasses
• Universality of the nonphononic vibrational spectrum across different classes of computer glasses
• Anomalous vibrational properties in the continuum limit of glasses
• Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses
• Probing the non-Debye low frequency excitations in glasses through random pinning
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• Soft Modes, Localization and Two-Level Systems in Spin Glasses
• Low-frequency vibrational spectrum of mean-field disordered systems
• Renormalization group theory for finite-size scaling in extreme statistics
• Universal low-frequency vibrational modes in silica glasses
• Mean-field model for the density of states of jammed soft spheres
• Low-frequency vibrations of jammed packings in large spatial dimensions
• The de Almeida-Thouless line in vector spin glasses
• A random matrix definition of the boson peak
• Robustness of Density of Low Frequency States in Amorphous Solids
• Mean-field model of interacting quasilocalized excitations in glasses
• Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices
• Approximating the XY model on a random graph with a $q$-state clock model
• Thermal origin of quasi-localised excitations in glasses
• The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
• The metastable minima of the Heisenberg spin glass in a random magnetic field
• Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for the spin glass XY model in a field on sparse random graphs

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• Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass
• Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems
• Low energy excitations of mean-field glasses
• Field theory for zero temperature soft anharmonic spin glasses in a field
• Exact numerical solution of the fully-connected classical and quantum Heisenberg spin glass
• The Spectral Boundary of Block Structured Random Matrices
• Analytical solution to Heisenberg spin glass models on sparse random graphs and their de Almeida-Thouless line
• Soft modes in vector spin glass models on sparse random graphs
• Statistical mechanics of vector Hopfield network near and above saturation