Glass and polycrystal states in a lattice spin model

We numerically study a nondisordered lattice spin system with a first order liquid-crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and it displays a dynamic phenomenology analogous to fragile supercooled liquids, with stretched exponential relaxation, power law increase of the relaxation time and high fragility index. At an effective spinodal temperature Tsp the relaxation time exceeds the crystal nucleation time, and the supercooled liquid loses stability. Below Tsp liquid properties cannot be extrapolated, in line with Kauzmann's scenario of a `lower metastability limit' of supercooled liquids as a solution of Kauzmann's paradox. The off-equilibrium dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal droplets, followed by extremely slow growth, due to the presence of pinning energy barriers. In the early time region, which is longer the lower the temperature, this crystal-growth phase is indistinguishable from an off-equilibrium glass, both from a structural and a dynamical point of view: crystal growth has not advanced enough to be structurally detectable, and a violation of the fluctuation-dissipation theorem (FDT) typical of structural glasses is observed. On the other hand, for longer times crystallization reaches a threshold beyond which crystal domains are easily identified, and FDT violation becomes compatible with ordinary domain growth.Comment: 25 page

Specific heat anomaly in a supercooled liquid with amorphous boundary conditions

We study the specific heat of a model supercooled liquid confined in a spherical cavity with amorphous boundary conditions. We find the equilibrium specific heat has a cavity-size-dependent peak as a function of temperature. The cavity allows us to perform a finite-size scaling (FSS) analysis, which indicates that the peak persists at a finite temperature in the thermodynamic limit. We attempt to collapse the data onto a FSS curve according to different theoretical scenarios, obtaining reasonable results in two cases: a "not-so-simple" liquid with nonstandard values of the exponents {\alpha} and {\nu}, and random first-order theory, with two different length scales.Comment: Includes Supplemental Materia

Response to "Comment on Static correlations functions and domain walls in glass-forming liquids: The case of a sandwich geometry" [J. Chem. Phys. 144, 227101 (2016)]

The point-to-set correlation function has proved to be a very valuable tool to probe structural correlations in disordered systems, but more than that, its detailed behavior has been used to try to draw information on the mechanisms leading to glassy behavior in supercooled liquids. For this reason it is of primary importance to discern which of those details are peculiar to glassy systems, and which are general features of confinement. Within the present response we provide an answer to the concerns raised in [J. Chem. Phys. 144, 227101 (2016)]

Ageing and crystallization in a lattice glass model

We have studied a the 3-$d$ lattice glass of Pica Ciamarra, Tarzia, de Candia and Coniglio [Phys.\ Rev.\ E. 67, 057105 (2013)], which has been shown to reproduce several features of the structural glass phenomenology, such as the cage effect, exponential increase of relaxation times and ageing. We show, using short-time dynamics, that the metastability limit is above the estimated Kauzmann temperature. We also find that in the region where the metastable liquid exists the aging exponent is lower that 0.5, indicating that equilibrium is reached relatively quickly. We conclude that the usefulness of this model to study the deeply supercooled regime is rather limited.Comment: 7 pages, 9 figure

Silent Flocks

Experiments find coherent information transfer through biological groups on length and time scales distinctly below those on which asymptotically correct hydrodynamic theories apply. We present here a new continuum theory of collective motion coupling the velocity and density fields of Toner and Tu to the inertial spin field recently introduced to describe information propagation in natural flocks of birds. The long-wavelength limit of the new equations reproduces Toner-Tu theory, while at shorter wavelengths (or, equivalently, smaller damping), spin fluctuations dominate over density fluctuations and second sound propagation of the kind observed in real flocks emerges. We study the dispersion relation of the new theory and find that when the speed of second sound is large, a gap sharply separates first from second sound modes. This gap implies the existence of `silent' flocks, namely medium-sized systems across which neither first nor second sound can propagate

Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids

There is a certain consensus that the very fast growth of the relaxation time $\tau$ occurring in glass-forming liquids on lowering the temperature must be due to the thermally activated rearrangement of correlated regions of growing size. Even though measuring the size of these regions has defied scientists for a while, there is indeed recent evidence of a growing correlation length $\xi$ in glass-formers. If we use Arrhenius law and make the mild assumption that the free-energy barrier to rearrangement scales as some power $\psi$ of the size of the correlated regions, we obtain a relationship between time and length, $T\log\tau \sim \xi^\psi$. According to both the Adam-Gibbs and the Random First Order theory the correlation length grows as $\xi \sim (T-T_k)^{-1/(d-\theta)}$, even though the two theories disagree on the value of $\theta$. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents $\psi$ and $\theta$ through the relationship $T\log\tau \sim (T-T_k)^{-\psi/(d-\theta)}$. Despite a few theoretical speculations, up to now there has been no experimental determination of these two exponents. Here we measure them numerically in a model glass-former, finding $\psi=1$ and $\theta=2$. Surprisingly, even though the values we found disagree with most previous theoretical suggestions, they give back the well-known VFT law for the relaxation time, $T\log\tau \sim (T-T_k)^{-1}$.Comment: 9 pages, 8 figure