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We study the energy minima of the fully-connected $m$-components vector spin glass model at zero temperature in an external magnetic field for $mge 3$. 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 $Nle 2048$ and compute the spectral properties, that show very strong corrections to the asymptotic scaling approaching the critical point.
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids.
The anharmonic soft modes studied in recent numerical work in the glass phase of simple liquids have an unstable core, stabilized by the positive restoring forces of the surrounding elastic medium. The present paper formulates an unstable core versio
Disconnectivity graphs are used to visualize the minima and the lowest energy barriers between the minima of complex systems. They give an easy and intuitive understanding of the underlying energy landscape and, as such, are excellent tools for under
The strain field surrounding the center of low frequency vibrational modes is analyzed for numerically created binary glasses with a 1/r^10 repulsive interatomic potential. Outside the unstable inner core of five to twenty atoms, one finds a mixture
We investigate the properties of local minima of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential which serves as a model of low temperature molecular or soft glasses. We track the long time grad