Low-temperature Anomalies Of Glasses Research Articles

Marginal stability of soft anharmonic mean field spin glasses

We investigate the properties of the glass phase 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 solve the model using mean field theory and show that, at low temperatures, it is described by full replica symmetry breaking. As a consequence, at zero temperature the glass phase is marginally stable. We show that in this case, marginal stability comes from a combination of both soft linear excitations—appearing in a gapless spectrum of the Hessian of linear excitations—and pseudogapped non-linear excitations—corresponding to nearly degenerate two level systems. Therefore, this model is a natural candidate to describe what happens in soft glasses, where quasi localized soft modes in the density of states appear together with non-linear modes triggering avalanches and conjectured to be essential to describe the universal low temperature anomalies of glasses.

Aging, Jamming, and the Limits of Stability of Amorphous Solids.

Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily far away from equilibrium and require a description of the history of the conditions under which they formed. In this paper we describe how the locality of interactions intrinsic to finite-dimensional systems affects the stability of amorphous solids far off equilibrium. Our analysis encompasses both structural glasses formed by cooling and colloidal assemblies formed by compression. A diagram outlining regions of marginal stability can be adduced which bears some resemblance to the quasi-equilibrium replica meanfield theory phase diagram of hard sphere glasses in high dimensions but is distinct from that construct in that the diagram describes not true phase transitions but kinetic transitions that depend on the preparation protocol. The diagram exhibits two distinct sectors. One sector corresponds to amorphous states with relatively open structures, the other to high density, more closely packed ones. The former transform rapidly owing to there being motions with no free energy barriers; these motions are string-like locally. In the dense region, amorphous systems age via compact activated reconfigurations. The two regimes correspond, in equilibrium, to the collisional or uniform liquid and the so-called landscape regime, respectively. These are separated by a spinodal line of dynamical crossovers. Owing to the rigidity of the surrounding matrix in the landscape, high-density part of the diagram, a sufficiently rapid pressure quench adds compressive energy which also leads to an instability toward string-like motions with near vanishing barriers. Conversely, a dilute collection of rigid particles, such as a colloidal suspension leads, when compressed, to a spatially heterogeneous structure with percolated mechanically stable regions. This jamming corresponds to the onset of activation when the spinodal line is traversed from the low density side. We argue that a stable glass made of sufficiently rigid particles can also be viewed as exhibiting sporadic and localized buckling instabilities that result in local jammed structures. The lines of instability we discuss resemble the Gardner transition of meanfield systems but, in contrast, do not result in true criticality owing to being short-circuited by activated events. The locally marginally stable modes of motion in amorphous solids correspond to secondary relaxation processes in structural glasses. Their relevance to the low temperature anomalies in glasses is also discussed.

Orientationally Disordered Crystals as Benchmark Models to Understand Low-Temperature Anomalies of Glasses

We compare the departure from gaussian (harmonic) behavior of the dynamic structure factors of a sample showing two glassy phases one of those being an orientationally-disordered crystal. The deviations from harmonic behavior of the amorphous phase and disordered crystal are found to be remarkably close. Such proximity enables us to take advantage of the crystal symmetry to relate specific details of the inter-particle potential to the non-gaussian effects characteristic of glassy matter.

Spin-glass approach to low-temperature anomalies in glasses

We discuss a spin-glass-type approach to the physics of structural glasses, which leads to a class of models that exhibit both glassy low-temperature phases and double- and single-well configurations in their potential energy landscape. The low-temperature anomalies characteristic of amorphous systems are reproduced, and within our model the universality issue can be illuminated. We consider the interaction between localized excitations and phonons, and we present a general expression for the dynamic susceptibility, from which dynamic properties such as the internal friction can be calculated.

Low-temperature anomalies of glasses: What can we learn from computer simulations?

We show that computer simulations can be used to obtain microscopic information about the nature of the soft modes which are believed to be responsible for the low-temperature anomalies. We derive the low-temperature properties from first principles. Furthermore, we obtain new information about the question as to how sensitively the anomalies depend on the microscopic structure.

Microscopic nature of tunneling states in glasses

For a simple two-dimensional model glass the total energy surface is analyzed by a systematic search for all local energy minima and subsequent determination of the distances between all minima in configuration space. Via a suitable projection on a one-dimensional potential one can clearly see how the local doublewell potentials (tunneling systems) which are responsible for the low-temperature anomalies of glasses are embedded in the total energy surface.

Relaxational and vibrational contributions to the dynamics of the glass transition

The low-frequency Raman spectra of a few glass forming liquids were analysed. It is shown that the main difference of the spectra for strong and fragile glass formers is the ratio of vibrational to relaxation contributions: the stronger the glass former, the higher is the vibrational contribution. It is shown that this difference correlates with the difference in the low-temperature anomalies of glasses. The spectra are compared with the mode coupling theory predictions. Qualitatively the predicted behavior is observed in all cases, however, some quantitative disagreement is found.

Low-temperature properties and localized electronic states of glasses

The basic ideas and a number of results of the theory of low-energy excitations and localized electronic states, which are responsible for the universal low-temperature anomalies in glasses and unusual electronic properties of nonmetallic glasses, primarily glassy semiconductors, are reviewed. The basic hypotheses and models, previously proposed in this connection in order to explain the numerous empirical data, are discussed. Recently developed concepts regarding soft atomic configurations as a significant feature of the structure of glasses, determining new types of low-energy excitations in such anharmonic systems and of localized electronic states—self-trapped electron pairs with negative correlation energy, with very strong interelectronic attraction—are examined. The above-mentioned properties of glasses are analyzed on the basis of this theory and briefly compared with experiment. Some important problems in the theory of glasses are indicated.

Low-Temperature Anomalies in Glasses and the Related Study of Electron and Neutron Irradiated Quartz

Low-Temperature Anomalies in Glasses and the Related Study of Electron and Neutron Irradiated Quartz

On the nuclear spin lattice relaxation in dielectric glasses

Within the framework of a vibrational interpretation of the low-temperature anomalies in glasses, it is shown that the Zeeman transitions in quadrupole-perturbed spin systems occur more through direct rather than Raman processes. Our model provides qualitative agreement with published nuclear spin-lattice relaxation and specific-heat data in dielectric glasses.