Critical behaviour of large scale dynamical heterogeneities in glasses: a complete theory (original) (raw)
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Universal fluctuations in the relaxation of structural glasses
Eprint Arxiv 0811 3190, 2008
The presence of strong local fluctuations -- dynamical heterogeneities -- has been observed near the glass transitions of a wide variety of materials. Here we explore the possible presence of universality in those fluctuations. We compare the statistical properties of fluctuations obtained from numerical simulations of four different glass-forming systems: two polymer systems and two particle systems. We find strong evidence for universality, both in the qualitative behavior of the fluctuations and in the remarkable agreement of the scaling functions describing them.
Critical dynamical heterogeneities close to continuous second-order glass transitions
2014
We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance ǫ from continuous second-order glass transitions. We find that the dynamical correlation length ξ behaves generically as ǫ −1/3 and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where ξ grows with time as ln 2 t exactly at criticality. All these results suggest a deep analogy between the glassy behaviour of attractive colloids or randomly pinned supercooled liquids and that of the Random Field Ising Model.
2010
Dynamical heterogeneities -- strong fluctuations near the glass transition -- are believed to be crucial to explain much of the glass transition phenomenology. One possible hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data from four glass-forming models to construct coarse grained observables that probe the dynamical heterogeneity, and decompose the fluctuations of these observables into two transverse components associated with the postulated time-fluctuation soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and timescales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with the correlation volumes of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.
Fluctuations in the time variable and dynamical heterogeneity in glass-forming systems
Physical Review E, 2013
We test a hypothesis for the origin of dynamical heterogeneity in slowly relaxing systems, namely that it emerges from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. We do this by constructing coarse grained observables and decomposing the fluctuations of these observables into transverse components, which are associated with the postulated time-fluctuation soft modes, and a longitudinal component, which represents the rest of the fluctuations. Our test is performed on data obtained in simulations of four models of structural glasses. As the hypothesis predicts, we find that the time reparametrization fluctuations become increasingly dominant as temperature is lowered and timescales are increased. More specifically, the ratio between the strengths of the transverse fluctuations and the longitudinal fluctuations grows as a function of the dynamical susceptibility, χ4, which represents the strength of the dynamical heterogeneity; and the correlation volumes for the transverse fluctuations are approximately proportional to those for the dynamical heterogeneity, while the correlation volumes for the longitudinal fluctuations remain small and approximately constant.
Dynamical heterogeneity in active glasses is inherently different from its equilibrium behavior
arXiv (Cornell University), 2021
Activity-driven glassy dynamics, while ubiquitous in collective cell migration, intracellular transport, dynamics in bacterial and ant colonies, etc, also extends the scope and extent of the as-yet mysterious physics of glass transition. Active glasses are hitherto assumed to be qualitatively similar to their equilibrium counterparts at an effective temperature, Teff. Here we combine large-scale simulations and an analytical mode-coupling theory (MCT) for such systems and show that, in fact, an active glass is inherently different from an equilibrium glass. Although the relaxation dynamics can be equilibrium-like at a Teff, effects of activity on the dynamical heterogeneity (DH), which has emerged as a cornerstone of glassy dynamics, are quite nontrivial and complex. With no preexisting data, we employ four distinct methods for reliable estimates of the DH length scales. Our work shows active glasses exhibit dramatic growth of DH and systems with similar relaxation times and Teff can have widely varying DH. To theoretically study DH, we extend active MCT and find excellent agreement between the theory and simulation results. Our results question the supposedly central role of DH in glassy dynamics and can have fundamental significance even in equilibrium.
Spatially heterogeneous ages in glassy dynamics
2003
We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution in these systems: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators obtained for a given noise realization. We explain why the noise-averaged correlators describe the fingerprint of quenched disorder when it exists, while the coarse-grained correlators are linked to noise-induced mesoscopic fluctuations. We predict constraints on the distribution of the fluctuations of the coarse-grained quantities. In particular, we show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. A symmetry of the underlying theory, namely invariance under reparametrizations of the time coordinates, underlies these results. We establish a connection between the probabilities of spatial distributions of local coarse-grained quantities and the theory of dynamic random manifolds. We define, and discuss the behavior of, a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We characterize the fluctuations in the system in terms of their fractal properties. For concreteness, we present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems.
Glassy behaviour in disordered systems with nonrelaxational dynamics
Physical Review Letters, 1997
We show that a family of disordered systems with non-relaxational dynamics may exhibit "glassy" behavior at nonzero temperature, although such a behavior appears to be ruled out by a facevalue application of mean-field theory. Nevertheless, the roots of this behavior can be understood within mean-field theory itself, properly interpreted. Finite systems belonging to this family have a dynamical regime with a self-similar pattern of alternating periods of fast motion and trapping.
Role of fluctuations in the yielding transition of two-dimensional glasses
Physical Review Research, 2020
We numerically study yielding in two-dimensional glasses which are generated with a very wide range of stabilities by swap Monte Carlo simulations and then slowly deformed at zero temperature. We provide strong numerical evidence that stable glasses yield via a nonequilibrium discontinuous transition in the thermodynamic limit. A critical point separates this brittle yielding from the ductile one observed in less stable glasses. We find that two-dimensional glasses yield similarly to their three-dimensional counterparts but display larger sample-tosample disorder-induced fluctuations, stronger finite-size effects, and rougher spatial wandering of the observed shear bands. These findings strongly constrain effective theories of yielding.
Glass transition in systems without static correlations: a microscopic theory
Journal of Physics: Condensed Matter, 2003
We present a first step toward a microscopic theory for the glass transition in systems with trivial static correlations. As an example we have chosen N infinitely thin hard rods with length L, fixed with their centers on a periodic lattice with lattice constant a. Starting from the N-rod Smoluchowski equation we derive a coupled set of equations for fluctuations of reduced k-rod densities. We approximate the influence of the surrounding rods onto the dynamics of a pair of rods by introduction of an effective rotational diffusion tensor D(Ω 1 , Ω 2) and in this way we obtain a selfconsistent equation for D. This equation exhibits a feedback mechanism leading to a slowing down of the relaxation. It involves as an input the Laplace transform υ 0 (l/r) at z = 0, l = L/a, of a torque-torque correlator of an isolated pair of rods with distance R = ar. Our equation predicts the existence of a continuous ergodicity-breaking transition at a critical length l c = L c /a. To estimate the critical length we perform an approximate analytical calculation of υ 0 (l/r) based on a variational approach and obtain l var c ∼ = 5.68, 4.84 and 3.96 for an sc, bcc and fcc lattice. We also evaluate υ 0 (l/r) numerically exactly from a two-rod simulation. The latter calculation leads to l num c ∼ = 3.45, 2.78 and 2.20 for the corresponding lattices. Close to l c the rotational diffusion constant decreases as D(l) ∼ (l c − l) γ with γ = 1 and a diverging time scale t ǫ ∼ |l c − l| −δ , δ = 2, appears. On this time scale the t-and l-dependence of the 1-rod density is determined by a master function depending only on t/t ǫ. In contrast to present microscopic theories our approach predicts a glass transition despite the absence of any static correlations.
1999
We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free energy. By exploiting this fact, we define a new order parameter function, and we relate it to the ratio between response and fluctuation, which is in principle measurable in an aging experiment. For a class of systems possessing stochastic stability, we show that this new order parameter function is intimately related to the static order parameter function, describing the distribution of overlaps between clustering states. The same method is applied to investigate the geometrical organization of pure states. We show that the ultrametric organization in the dynamics implies static ultrametricity, and we relate these properties to static separability, i.e., the property that the measure of the overlap between pure states is essentially unique. Our results, especially relevant for spin glasses, pave the way to an experimental determination of the order parameter function.