The dynamical structure factor in disordered systems

We study the spectral width as a function of the external momentum for the dynamical structure factor of a disordered harmonic solid, considered as a toy model for supercooled liquids and glasses. Both in the context of single-link coherent potential approximation and of a single-defect approximation, two different regimes are clearly identified: if the density of states at zero energy is zero, the Rayleigh $p^4$ law is recovered for small momentum. On the contrary, if the disorder induces a non vanishing density of states at zero energy, a linear behaviour is obtained. The dynamical structure factor is numerically calculated in lattices as large as $96^3$, and satisfactorily agrees with the analytical computations.Comment: 7 pages plus 4 postscript figure

Finite size effects in the specific heat of glass-formers

We report clear finite size effects in the specific heat and in the relaxation times of a model glass former at temperatures considerably smaller than the Mode Coupling transition. A crucial ingredient to reach this result is a new Monte Carlo algorithm which allows us to reduce the relaxation time by two order of magnitudes. These effects signal the existence of a large correlation length in static quantities.Comment: Proceeding of "3rd International Workshop on Complex Systems". Sendai (Japan). To appear on AIP Conference serie

Optimized Monte Carlo Method for glasses

A new Monte Carlo algorithm is introduced for the simulation of supercooled liquids and glass formers, and tested in two model glasses. The algorithm is shown to thermalize well below the Mode Coupling temperature and to outperform other optimized Monte Carlo methods. Using the algorithm, we obtain finite size effects in the specific heat. This effect points to the existence of a large correlation length measurable in equal time correlation functions.Comment: Proceedings of "X International workshop on Disordered Systems" held in Molveno (Italy), March 200

On the critical behavior of the specific heat in glass-formers

We show numeric evidence that, at low enough temperatures, the potential energy density of a glass-forming liquid fluctuates over length scales much larger than the interaction range. We focus on the behavior of translationally invariant quantities. The growing correlation length is unveiled by studying the Finite Size effects. In the thermodynamic limit, the specific heat and the relaxation time diverge as a power law. Both features point towards the existence of a critical point in the metastable supercooled liquid phase.Comment: Version to be published in Phys. Rev.

Vibrational spectra in glasses

The findings of X-ray and neutron scattering experiments on amorphous systems are interpreted within the framework of the theory of Euclidean random matrices. This allows to take into account the topological nature of the disorder, a key ingredient which strongly affects the vibrational spectra of those systems. We present a resummation scheme for a perturbative expansion in the inverse particle density, allowing an accurate analytical computation of the dynamical structure factor within the range of densities encountered in real systems.Comment: Talk given at the '8th International Workshop on Disordered Systems' Andalo, Trento, 12-15 March 200

Vibrations in glasses and Euclidean Random Matrix theory

We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peak and secondary peak), the Euclidean random matrix theory provide a single and fairly simple theoretical framework to their explanation.Comment: 11 pages, 7 postscript figures, Proceedings of Statphys 2

Static correlations functions and domain walls in glass-forming liquids: the case of a sandwich geometry

The problem of measuring nontrivial static correlations in deeply supercooled liquids made recently some progress thanks to the introduction of amorphous boundary conditions, in which a set of free particles is subject to the effect of a different set of particles frozen into their (low temperature) equilibrium positions. In this way, one can study the crossover from nonergodic to ergodic phase, as the size of the free region grows and the effect of the confinement fades. Such crossover defines the so-called point-to-set correlation length, which has been measured in a spherical geometry, or cavity. Here, we make further progress in the study ofcorrelations under amorphous boundary conditions by analyzing the equilibrium properties of a glass-forming liquid, confined in a planar ("sandwich") geometry. The mobile particles are subject to amorphous boundary conditions with the particles in the surrounding walls frozen into their low temperature equilibrium configurations. Compared to the cavity, the sandwich geometry has three main advantages: i) the width of the sandwich is decoupled from its longitudinal size, making the thermodynamic limit possible; ii) for very large width, the behaviour off a single wall can be studied; iii) we can use "anti-parallel" boundary conditions to force a domain wall and measure its excess energy. Our results confirm that amorphous boundary conditions are indeed a very useful new tool inthe study of static properties of glass-forming liquids, but also raise some warning about the fact that not all correlation functions that can be calculated in this framework give the same qualitative results.Comment: Submited to JCP special issue on the glass transisio

The Boson peak and the phonons in glasses

Despite the presence of topological disorder, phonons seem to exist also in glasses at very high frequencies (THz) and they remarkably persist into the supercooled liquid. A universal feature of such a systems is the Boson peak, an excess of states over the standard Debye contribution at the vibrational density of states. Exploiting the euclidean random matrix theory of vibrations in amorphous systems we show that this peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point dominated phase (without phonons). The theoretical predictions are checked by means of numeric simulations.Comment: to appear in the proceedings of the conference "Slow dynamics in complex sistems", Sendai (Japan) 200

Numerical simulations of liquids with amorphous boundary conditions

It has recently become clear that simulations under amorphpous boundary conditions (ABCs) can provide valuable information on the dynamics and thermodynamics of disordered systems with no obvious ordered parameter. In particular, they allow to detect a correlation length that is not measurable with standard correlation functions. Here we explain what exactly is meant by ABCs, discuss their relation with point-to-set correlations and briefly describe some recent results obtained with this technique.Comment: Presented at STATPHYS 2