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Register a new userGlass-specific behavior in the damping of acoustic-like vibrations
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High frequency sound is observed in lithium diborate glass, Li$_2$O--2B$_2$O$_3$, using Brillouin scattering of light and x-rays. The sound attenuation exhibits a non-trivial dependence on the wavevector, with a remarkably rapid increase towards a Ioffe-Regel crossover as the frequency approaches the boson peak from below. An analysis of literature results reveals the near coincidence of the boson-peak frequency with a Ioffe-Regel limit for sound in {em all} sufficiently strong glasses. We conjecture that this behavior, specific to glassy materials, must be quite universal among them.
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A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204 (2012), arXiv:1206:0783] compares the low-temperature phase of the 3D Edwards-Anderson (EA) model to its mean-field counterpart, the Sherrington-Kirkpatrick (SK) model. The authors study the overlap distributions P_J(q) and conclude that the two models behave differently. Here we notice that a similar analysis using state-of-the-art, larger data sets for the EA model (generated with the Janus computer) leads to a very clear interpretation of the results of Yucesoy et al., showing that the EA model behaves as predicted by the replica symmetry breaking (RSB) theory.
The dynamic structure factor of lithium-diborate glass has been measured at several values of the momentum transfer $Q$ using high resolution inelastic x-ray scattering. Much attention has been devoted to the low $Q$-range, below the observed Ioffe-Regel crossover qco{}$simeq$ 2.1 nm$^{-1}$. We find that below qco{}, the linewidth of longitudinal acoustic waves increases with a high power of either $Q$, or of the frequency $Omega$, up to the crossover frequency OMco{} $simeq$ 9 meV that nearly coincides with the center of the boson peak. This new finding strongly supports the view that resonance and hybridization of acoustic waves with a distribution of rather local low frequency modes forming the boson peak is responsible for the end of acoustic branches in strong glasses. Further, we present high resolution Brillouin light-scattering data obtained at much lower frequencies on the same sample. These clearly rule out a simple $Omega^2$-dependence of the acoustic damping over the entire frequency range.
In Phys. Rev. Lett. 110, 219701 (2013) [arXiv:1211.0843] Billoire et al. criticize the conclusions of our Letter [Phys. Rev. Lett. 109, 177204 (2012), arxiv:1206.0783]. They argue that considering the Edwards-Anderson and Sherrington-Kirkpatrick models at the same temperature is inappropriate and propose an interpretation based on the replica symmetry breaking theory. Here we show that the theory presented in the Comment does not explain our data on the Edwards-Anderson spin glass and we stand by our assertion that the low-temperature behavior of the Edwards-Anderson spin glass model does not appear to be mean-field like.
In amorphous solids, a non-negligible part of thermal conductivity results from phonon scattering on the structural disorder. The conversion of acoustic energy into thermal energy is often measured by the Dynamical Structure Factor (DSF) thanks to inelastic neutron or X-Ray scattering. The DSF is used to quantify the dispersion relation of phonons, together with their damping. However, the connection of the dynamical structure factor with dynamical attenuation of wave packets in glasses is still a matter of debate. We focus here on the analysis of wave packets propagation in numerical models of amorphous silicon. We show that the DHO fits (Damped Harmonic Oscillator model) of the dynamical structure factors give a good estimate of the wave packets mean-free path, only below the Ioffe-Regel limit. Above the Ioffe-Regel limit and below the mobility edge, a pure diffusive regime without a definite mean free path is observed. The high-frequency mobility edge is characteristic of a transition to localized vibrations. Below the Ioffe-Regel criterion, a mixed regime is evidenced at intermediate frequencies, with a coexistence of propagative and diffusive wave fronts. The transition between these different regimes is analyzed in details and reveals a complex dynamics for energy transportation, thus raising the question of the correct modeling of thermal transport in amorphous materials.
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.
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