Are defect models consistent with the entropy and specific heat of glass-formers?

We show that point-like defect model of glasses cannot explain thermodynamic properties of glass-formers, as for example the excess specific heat close to the glass transition, contrary to the claim of J.P. Garrahan, D. Chandler [Proc. Natl. Acad. Sci. 100, 9710 (2003)]. More general models and approaches in terms of extended defects are also discussed.Comment: 4 pages, version to appear in J. Chem. Phys with a Note Adde

Super-diffusion around the rigidity transition: Levy and the Lilliputians

By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a genuine Levy flight, but with `jump' size very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.Comment: 7 pages, 6 figure

Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass

The dynamical properties of a dense horizontally vibrated bidisperse granular monolayer are experimentally investigated. The quench protocol produces states with a frozen structure of the assembly, but the remaining degrees of freedom associated with contact dynamics control the appearance of macroscopic rigidity. We provide decisive experimental evidence that this transition is a critical phenomenon, with increasingly collective and heterogeneous rearrangements occurring at length scales much smaller than the grains' diameter, presumably reflecting the contact force network fluctuations. Dynamical correlation time and length scales soar on both sides of the transition, as the volume fraction varies over a remarkably tiny range ($\delta \phi/\phi \sim 10^{-3}$). We characterize the motion of individual grains, which becomes super-diffusive at the jamming transition $\phi_J$, signaling long-ranged temporal correlations. Correspondingly, the system exhibits long-ranged four-point dynamical correlations in space that obey critical scaling at the transition density.Comment: 4 pages, 8 figure

Critical fluctuations and breakdown of Stokes-Einstein relation in the Mode-Coupling Theory of glasses

We argue that the critical dynamical fluctuations predicted by the mode-coupling theory (MCT) of glasses provide a natural mechanism to explain the breakdown of the Stokes-Einstein relation. This breakdown, observed numerically and experimentally in a region where MCT should hold, is one of the major difficulty of the theory, for which we propose a natural resolution based on the recent interpretation of the MCT transition as a bona fide critical point with a diverging length scale. We also show that the upper critical dimension of MCT is d_c=8.Comment: Proceedings of the workshop on non-equilibrium phenomena in supercooled fluids, glasses and amorphous materials (17-22 September, 2006, Pisa

Mode-Coupling as a Landau Theory of the Glass Transition

We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value. This sheds light on the universality of MCT predictions. While our expansion generates higher order non-local corrections that modify the standard MCT equations, we find that the square root singularity of the order parameter, the scaling function in the \beta regime and the functional relation between the exponents defining the \alpha and \beta timescales are universal and left intact by these corrections.Comment: 6 pages, 1 figure, submitted to EPL; corrected typos in the abstract; corrected minor typo in reference

Evidence of growing spatial correlations at the glass transition from nonlinear response experiments

The ac nonlinear dielectric response $\chi_3(\omega,T)$ of glycerol was measured close to its glass transition temperature $T_g$ to investigate the prediction that supercooled liquids respond in an increasingly non-linear way as the dynamics slows down (as spin-glasses do). We find that $\chi_3(\omega,T)$ indeed displays several non trivial features. It is peaked as a function of the frequency $\omega$ and obeys scaling as a function of $\omega \tau(T)$, with $\tau(T)$ the relaxation time of the liquid. The height of the peak, proportional to the number of dynamically correlated molecules $N_{corr}(T)$, increases as the system becomes glassy, and $\chi_3$ decays as a power-law of $\omega$ over several decades beyond the peak. These findings confirm the collective nature of the glassy dynamics and provide the first direct estimate of the $T$ dependence of $N_{corr}$.Comment: 22 pages, 6 figures. With respect to v1, a few new sentences were added in the introduction and conclusion, references were updated, some typos corrected

Non-linear susceptibility in glassy systems: a probe for cooperative dynamical length scales

We argue that for generic systems close to a critical point, an extended Fluctuation-Dissipation relation connects the low frequency non-linear (cubic) susceptibility to the four-point correlation function. In glassy systems, the latter contains interesting information on the heterogeneity and cooperativity of the dynamics. Our result suggests that if the abrupt slowing down of glassy materials is indeed accompanied by the growth of a cooperative length ell, then the non-linear, 3 omega response to an oscillating field should substantially increase and give direct information on the temperature (or density) dependence of ell. The analysis of the non-linear compressibility or the dielectric susceptibility in supercooled liquids, or the non-linear magnetic susceptibility in spin-glasses, should give access to a cooperative length scale, that grows as the temperature is decreased or as the age of the system increases. Our theoretical analysis holds exactly within the Mode-Coupling Theory of glasses.Comment: 12 pages, 3 figures; a careful discussion of the spin-glass case in a field adde

Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations

We study in detail the predictions of various theoretical approaches, in particular mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wavevector dependence of multi-point correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multi-point correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multi-point correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.Comment: 23 pages, 12 fig

Spectral Density of Sparse Sample Covariance Matrices

Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form $J = A^{\rm T} A$, where $A$ is an $M \times N$ real sparse random matrix. The difference from a dense random matrix is the most significant in the tail region of the spectrum. We compare the results of several approximation schemes, focusing on the behavior in the tail region.Comment: 22 pages, 4 figures, minor corrections mad