Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDelocalization transition in low energy excitation modes of vector spin glasses
92
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic 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 $mge 3$. 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.
rate research
Read More
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. Recent simulational studies suggest that the density of the excess modes scales with their frequency $omega$ as $omega^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_text{exc}(omega)sim omega^2 $ up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of $D_text{exc}(omega)$ correlates with the stability dependence of low-frequency sound attenuation. However, we also find that in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode there are excess modes with a system size independent density of states that scales as $omega^3$.
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 version of the phenomenological soft potential model for the low temperature anomalies of glasses, relates a new numerical finding on low-barrier relaxations to old soft potential model results, and discusses experimental evidence for an unstable core of the boson peak modes.
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 understanding the complexity involved in finding low-lying or global minima of such systems. We have developed a classification scheme that categorizes highly-degenerate minima of spin glasses based on similarity and accessibility of the individual states. This classification allows us to condense the information pertained in different dales of the energy landscape to a single representation using color to distinguish its type and a bar chart to indicate the average size of the dales at their respective energy levels. We use this classification to visualize disconnectivity graphs of small representations of different tile-planted models of spin glasses. An analysis of the results shows that different models have distinctly different features in the total number of minima, the distribution of the minima with respect to the ground state, the barrier height and in the occurrence of the different types of minimum energy dales.
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 of a motion similar to the string motion in the core with the strain field of three oscillating elastic dipoles in the center. The additional outside string motion contributes more to the stabilization of the core than the strain field, but the strain field dominates at long distances, in agreement with recent numerical findings. The small restoring force of the outside string motion places its average frequency close to the boson peak. The average creation energy of a soft mode in this binary glass is about 2.5 times the thermal energy at the freezing temperature. Scaling the soft potential parameters of the numerical modes to metallic glasses, one finds quantitative agreement with measurements of the sound absorption by tunneling states at low temperatures and by the excess modes at the boson peak.
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 gradient descent dynamics in the glassy phase through dynamical mean field theory and show that spins are separated in two groups depending on their local stiffness. For spins having local stiffness that is right above its smallest possible value, the local fields distribution displays a depletion around the origin while those having a stiffness right below its largest possible value have a regular local fields distribution. We rationalize these findings through the replica method and show that the finite temperature phase transition to the glass phase is of continuous (full) replica-symmetry-breaking (RSB) type at low temperatures, down to zero temperature. Furthermore, marginal stability of the zero temperature fullRSB solution implies a linear pseudogap in the density of cavity fields for the spins with a local effective stiffness that is below a certain threshold. This generates a hole around the origin in the corresponding local field distribution. Those spins are natural candidates to model two level systems (TLS). The behavior of the cavity fields distribution for spins having stiffness close to the threshold one determines the tail of the low frequency density of states which is gapless. Therefore the corresponding spins are the natural candidates to model quasi localized modes (QLM) in glasses.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
