Elasticity and metastability limit in supercooled liquids: a lattice model

We present Monte Carlo simulations on a lattice system that displays a first order phase transition between a disordered phase (liquid) and an ordered phase (crystal). The model is augmented by an interaction that simulates the effect of elasticity in continuum models. The temperature range of stability of the liquid phase is strongly increased in the presence of the elastic interaction. We discuss the consequences of this result for the existence of a kinetic spinodal in real systems.Comment: 8 pages, 5 figure

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

Role of saddles in mean-field dynamics above the glass transition

Recent numerical developments in the study of glassy systems have shown that it is possible to give a purely geometric interpretation of the dynamic glass transition by considering the properties of unstable saddle points of the energy. Here we further develop this program in the context of a mean-field model, by analytically studying the properties of the closest saddle point to an equilibrium configuration of the system. We prove that when the glass transition is approached the energy of the closest saddle goes to the threshold energy, defined as the energy level below which the degree of instability of the typical stationary points vanishes. Moreover, we show that the distance between a typical equilibrium configuration and the closest saddle is always very small and that, surprisingly, it is almost independent of the temperature

Coarsening Dynamics of a Nonconserved Field Advected by a Uniform Shear Flow

We consider the ordering kinetics of a nonconserved scalar field advected by a uniform shear flow. Using the Ohta-Jasnow-Kawasaki approximation, modified to allow for shear-induced anisotropy, we calculate the asymptotic time dependence of the characteristic length scales, L_parallel and L_perp, that describe the growth of order parallel and perpendicular to the mean domain orientation. In space dimension d=3 we find, up to constants, L_parallel = gamma t^{3/2}, L_perp = t^{1/2}, where gamma is the shear rate, while for d = 2 we find L_parallel = gamma^{1/2} t (ln t)^{1/4}, L_perp = gamma^{-1/2}(ln t)^{-1/4} . Our predictions for d=2 can be tested by experiments on twisted nematic liquid crystals.Comment: RevTex, 4 page

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)]

Dynamic relaxation of a liquid cavity under amorphous boundary conditions

The growth of cooperatively rearranging regions was invoked long ago by Adam and Gibbs to explain the slowing down of glass-forming liquids. The lack of knowledge about the nature of the growing order, though, complicates the definition of an appropriate correlation function. One option is the point-to-set correlation function, which measures the spatial span of the influence of amorphous boundary conditions on a confined system. By using a swap Monte Carlo algorithm we measure the equilibration time of a liquid droplet bounded by amorphous boundary conditions in a model glass-former at low temperature, and we show that the cavity relaxation time increases with the size of the droplet, saturating to the bulk value when the droplet outgrows the point-to-set correlation length. This fact supports the idea that the point-to-set correlation length is the natural size of the cooperatively rearranging regions. On the other hand, the cavity relaxation time computed by a standard, nonswap dynamics, has the opposite behavior, showing a very steep increase when the cavity size is decreased. We try to reconcile this difference by discussing the possible hybridization between MCT and activated processes, and by introducing a new kind of amorphous boundary conditions, inspired by the concept of frozen external state as an alternative to the commonly used frozen external configuration.Comment: Completely rewritten version. After the first submission it was realized that swap and nonswap dynamics results are qualitatively different. This version reports the results of both dynamics and discusses the different behaviors. 17 pages, 18 figure

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

Geometric approach to the dynamic glass transition

We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative change in the topological properties of the landscape. Furthermore, we show that the potential energy barriers connecting local glassy minima increase with decreasing energy of the minima, and we relate this behaviour to the fragility of the system. Finally, we analyze the real space structure of activated processes by studying the distribution of particle displacements for local minima connected by simple saddles