Glasses and disordered materials are known to display anomalous features in the density of states, in the specific heat and in thermal transport. Nevertheless, in recent years, the question whether these properties are really anomalous (and peculiar of disordered systems) or rather more universal than previously thought, has emerged. New experimental and theoretical observations have questioned the origin of the boson peak and the linear in T specific heat exclusively from disorder and TLS. The same properties have been indeed observed in ordered or minimally disordered compounds and in incommensurate structures for which the standard explanations are not applicable. Using the formal analogy between phason modes (e.g. in quasicrystals and incommensurate lattices) and diffusons, and between amplitude modes and optical phonons, we suggest the existence of a more universal physics behind these properties. In particular, we strengthen the idea that linear in T specific heat is linked to low energy diffusive modes and that a BP excess can be simply induced by gapped optical-like modes.
By the adoption of a quaternion orientational order parameter to describe solidification, the topological origins of the thermal transport properties of crystalline and non-crystalline solid states are considered herein. Global orientational order, achieved by spontaneous symmetry breaking, is prevented at finite temperatures for systems that exist in restricted dimensions (Mermin-Wagner theorem). Just as complex ordered systems exist in restricted dimensions in 2D and 1D, owing to the dimensionality of the order parameter, quaternion ordered systems in 4D and 3D exist in restricted dimensions…
The low-temperature thermal and transport properties of an unusual kind of crystal exhibiting minimal molecular positional and tilting disorder have been measured. The material, namely, low-dimensional, highly anisotropic pentachloronitrobenzene (PCNB) has a layered structure of rhombohedral parallel planes in which the molecules execute large-amplitude in-plane as well as concurrent out-of-plane librational motions. Our study reveals that low-temperature glassy anomalies can be found in a system with minimal disorder due to the freezing of (mostly in-plane) reorientational jumps of molecules …
High-precision pressure measurements in solid 4He, grown by the capillary blocking technique, have been made in temperatures range from 50 to 500 mK. The temperature dependence of pressure indicates that aside from the usual phonon contribution ~T^4, there is an additional contribution ~ T^2, the latter becoming dominant at temperatures T < 300 mK, where an abnormal behavior attributed to supersolidity has been observed. The data suggest the appearance of a glassy phase (that might be responsible for the anomalous behaviors observed previously).
By using the glassy (helium-)fluid model and boundary perturbation method, we can obtain the velocity fields (as well as the flow rate; up to the second order) inside the wavy-rough cylindrical nanopores which are of the same size as those samples prepared by Kim and Chan as well as Day {\it et al.} Our results show that the velocities measured in porous Vycor samples could be reproduced by carefully selecting relevant parameters but those in glass capillaries are difficult to obtain.
Quantifying mechanical disorder in solids, either disordered crystals or glassy solids, and understanding its range of variability are of prime importance, e.g.~for discovering structure-properties relations. The bounds on the degree of mechanical fluctuations in disordered solids and how those depend on solids formation history remain unknown. Here, we study a broadly applicable quantifier of mesoscopic mechanical disorder $χ$, defined via the dimensionless fluctuations of the shear modulus, over a wide variety of disordered computer solids and upon varying different control parameters. $χ$ i…
A database of minima and transition states corresponds to a network where the minima represent nodes and the transition states correspond to edges between the pairs of minima they connect via steepest-descent paths. Here we construct networks for small clusters bound by the Morse potential for a selection of physically relevant parameters, in two and three dimensions. The properties of these unweighted and undirected networks are analysed to examine two features: whether they are small-world, where the shortest path between nodes involves only a small number or edges; and whether they are scal…
Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among different competing relaxation/kinetic processes. Here, two constitutive models of cage relaxation are examined within the microscopic model of nonaffine elasto-plasticity. One (widely used) constitutive model implies that the overall relaxation rate is dominated by the fastest between the structural ($α$) relaxation rate and the shear-induced relaxation rate. A dif…
Glasses at low temperature fluctuate around their inherent states; glassy anomalies reflect the structure of these states. Recently there have been numerous observations of long-range stress correlations in glassy materials, from supercooled liquids to colloids and granular materials, but without a common explanation. Herein it is shown, using a field theory of inherent states, that long-range stress correlations follow from mechanical equilibrium alone, with explicit predictions for stress correlations in 2 and 3 dimensions. `Equations of state' relating fluctuations to imposed stresses are d…
Structural glasses formed by quenching a melt are known to host a population of low-energy quasilocalized (nonphononic) excitations whose frequencies $ω$ follow a universal $\sim\!ω^4$ distribution as $ω\!\to\!0$, independently of the glass formation history, the interparticle interaction potential or spatial dimension. Here, we show that the universal quartic law of nonphononic excitations also holds in disordered crystals featuring finite long-range order, which is absent in their glassy counterparts. We thus establish that the degree of universality of the quartic law extends beyond structu…
Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-elastic modulus etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a funct…
We study 2D solids with weak substrate disorder, using Coulomb gas renormalisation. The melting transition is found to be replaced by a sharp crossover between a high $T$ liquid with thermally induced dislocations, and a low $T$ glassy regime with disorder induced dislocations at scales larger than $ξ_{d}$ which we compute ($ξ_{d}\gg R_{c}\sim R_{a}$, the Larkin and translational correlation lengths). We discuss experimental consequences, reminiscent of melting, such as size effects in vortex flow and AC response in superconducting films.
While soft quasilocalized vibrational modes are known to populate the low-frequency spectrum of glassy solids, their contribution to thermal properties is still not fully elucidated. We numerically show that, despite their spatially localized nature, these modes are as effective heat carriers as the delocalized ones and can contribute non-negligible to the total thermal conductivity in the low-temperature regime, especially for T < 0.05 Tg where Tg is the glass transition temperature. We further prove that the mutual coherence between the low-frequency quasilocalized modes and other modes expl…
The theory of glassy fluctuations can be formulated in terms of disordered effective potentials. While the properties of the average potentials are well understood, the study of the fluctuations has been so far quite limited. Close to the MCT transition, fluctuations induced by the dynamical heterogeneities in supercooled liquids can be described by a cubic field theory in presence of a random field term. In this paper we set up the general problem of the large deviations going beyond the assumption of the vicinity to $T_{MCT}$ and analyze it in the paradigmatic case of spherical ($p$-spin) gl…
We study the glassy super-rough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a newly developed minimum cost flow algorithm. Results for the height-height correlation function are compared with analytical and numerical predictions. The domain wall energy of a boundary induced step grows logarithmically with system size, indicating the marginal stability of the ground state, and the fractal dimension of the step is estimated. The sensibility of the ground state with respect to …
We model a planar array of fluxlines as a discrete solid-on-solid model with quenched disorder. Simulations at finite temperatures are made possible by a new algorithm which circumvents the slow glassy dynamics encountered by traditional Metropolis Monte Carlo algorithms. Numerical results on magnetic susceptibility variations support analytic predictions.
We review in this work specific-heat experiments, that we have conducted on different hydrogen-bonded glasses during last years. Specifically, we have measured the low-temperature specific heat Cp for a set of glassy alcohols: normal and fully-deuterated ethanol, 1- and 2- propanol, and glycerol. Ethanol exhibits a very interesting polymorphism presenting three different solid phases at low temperature: a fully-ordered (monoclinic) crystal, an orientationally-disordered (cubic) crystal or 'orientational glass', and the ordinary structural glass. By measuring and comparing the low-temperature s…
The low temperature acoustic and thermal properties of amorphous, glassy materials are remarkably similar. All these properties are described theoretically with reasonable quantitative accuracy by assuming that the amorphous solid contains dynamical defects that can be described at low temperatures as an ensemble of two-level systems (TLS), but the deep nature of these TLSs is not clarified yet. Moreover, glassy properties were found also in disordered crystals, quasicrystals, and even perfect crystals with a large number of atoms in the unit cell. In crystals, the glassy properties are not un…
We study the phase ordering dynamics of a two dimensional model colloidal solid using molecular dynamics simulations. The colloid particles interact with each other with a Hamaker potential modified by the presence of equatorial "patches" of attractive and negative regions. The total interaction potential between two such colloids is, therefore, strongly directional and has three-fold symmetry. Working in the canonical ensemble, we determine the tentative phase diagram in the density-temperature plane which features three distinct crystalline ground states viz, a low density honeycomb solid fo…
We use quantum Monte Carlo simulations with the worm algorithm to study the phase diagram of a two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated disorder in the hard-core limit. Our study shows the system is in a supersolid phase at weak disorder and a disordered solid phase at stronger disorder. Due to long-range interactions, a large region of metastable states exists in both clean and disordered systems. By comparing the phase diagrams for both clean and disordered systems, we find that disorder suppresses metastable states and superfluidity. W…
We argue that the intrinsic glassy degrees of freedom in amorphous solids giving rise to the thermal conductivity plateau and the ``boson peak'' in the heat capacity at moderately low temperatures are directly connected to those motions giving rise to the two-level like excitations seen at still lower temperatures. These degrees of freedom can be thought of as strongly anharmonic transitions between the local minima of the glassy energy landscape that are accompanied by ripplon-like domain wall motions of the glassy mosaic structure predicted to occur at $T_g$ by the random first order transit…
We consider temperature-induced melting of a Wigner solid in one dimensional (1D) and two dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we f…
Solid He4 is viewed as a nearly perfect Debye solid. Yet, recent calorimetry indicates that its low-temperature specific heat has both cubic and linear contributions. These features appear in the same temperature range ($T \sim 200$ mK) where measurements of the torsional oscillator period suggest a supersolid transition. We analyze the specific heat to compare the measured with the estimated entropy for a proposed supersolid transition with 1% superfluid fraction. We find that the experimental entropy is substantially less than the calculated entropy. We suggest that the low-temperature linea…
