Stochastic Beta Relaxation (SBR) is a model for the dynamics of glass- forming liquids close to the glass transition singularity of the idealized mode- coupling theory (MCT) that has been derived from generic MCT-like theories by applying dynamical field-theory techniques. SBR displays a rich phenomenology common to most super-cooled liquids. In its simplest version it naturally explains two prominent features of the dynamical crossover: the change from a power-law to exponential increase in the structural relaxation time and the violation of the Stokes-Einstein relation between diffusion and viscosity. The solution of the model in three dimensions unveils a qualitative change at the crossover in the structure of dynamical fluctuations from a regime characterized by power-law increases of their amplitude and size to a regime dominated by strong Dynamical Heterogeneities: rare regions where dynamics is relatively much faster than in the rest of the system. While the relaxation time changes by orders of magnitude, the size of these regions does not change significantly and actually decreases below the crossover temperature. SBR cannot sustain too large fluctuations and could fail well below the crossover temperature. There it could be replaced by non-conventional activated dynamics characterized by elementary events with intrinsic time and length scales of an unusual large (but not necessarily increasing) size (mesoscopic vs. microscopic).
Stochastic-Beta-Relaxation (SBR) provides a characterisation of the glass crossover in discontinuous Spin-Glasses and Supercoooled liquid. Notably it can be derived through a rigorous computation from a dynamical Landau theory. In this paper I will discuss the precise meaning of this connection in a language that does not require familiarity with statistical field theory. I will discuss finite-size corrections in mean-field Spin-Glass models and loop corrections in finite-dimensional models that are both described by the dynamical Landau theory considered. Then I will argue that the same Landa…
We discuss some generic features of the dynamics of glass-forming liquids close to the glass transition singularity of the idealized mode-coupling theory (MCT). The analysis is based on a recent model by one of the authors for the intermediate-time dynamics ($β$ relaxation), derived by applying dynamical field-theory techniques to the idealized MCT. Combined with the assumption of time-temperature superposition for the slow structural ($α$) relaxation, the model naturally explains three prominent features of the dynamical crossover: the change from a power-law to exponential increase in the st…
As shown by early studies on mean-field models of the glass transition, the geometrical features of the energy landscape provide fundamental information on the dynamical transition at the Mode-Coupling temperature $T_d$. We show that active particles can serve as a useful tool for gaining insight into the topological crossover in model glass-formers. In such systems the landmark of the minima-to-saddle transition in the potential energy landscape, taking place in the proximity of $T_d$, is the critical slowing down of dynamics. Nevertheless, the critical slowing down is a bottleneck for numeri…
By means of extensive computer simulations we analyze in detail the two dimensional $\pm J$ Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to ``spin glass'' like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the ``spin glass'' behavior to a paramagnetic phase for the largest volume studied.
The effect of long wavelength fluctuations on the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $β$ regime is studied by means of the standard field-theoretical procedure for a genuine second-order phase transition. The resulting perturbative loop expansion can be resummed leading to an extension of the MCT equation for the critical correlator with local random fluctuations of the separation parameter. The corresponding model explains both qualitatively and quantitatively why the MCT dynamical singularity is transformed into a crossover from relaxational to activated dynamic…
We study the equilibrium statistical properties of the potential energy landscape of several glass models in a temperature regime so far inaccessible to computer simulations. We show that unstable modes of the stationary points undergo a localization transition in real space close to the mode-coupling crossover temperature determined from the dynamics. The concentration of localized unstable modes found at low temperature is a non-universal, finite dimensional feature not captured by mean-field glass theory. Our analysis reconciles, and considerably expands, previous conflicting numerical resu…
An equilibrated model glass-forming liquid is studied by mapping successive configurations produced by molecular dynamics simulation onto a time series of inherent structures (local minima in the potential energy). Using this ``inherent dynamics'' approach we find direct numerical evidence for the long held view that below a crossover temperature, $T_x$, the liquid's dynamics can be separated into (i) vibrations around inherent structures and (ii) transitions between inherent structures (M. Goldstein, J. Chem. Phys. {\bf 51}, 3728 (1969)), i.e., the dynamics become ``dominated'' by the potenti…
I introduce a dynamical field theory to describe the glassy behavior in supercooled liquids. The mean-field approximation of the theory predicts a dynamical arrest transition, as in ideal Mode-Coupling-Theory and mean-field discontinuous Spin-Glass Models. Instead {\it beyond} the mean-field approximation the theory predicts that the transition is avoided and transformed into a crossover, as observed in experiments and simulations. To go beyond mean-field a standard perturbative loop expansion is performed at first. Approaching the ideal critical point this expansion is divergent at all orders…
The standard field-theoretical procedure to study the effect of long wavelength fluctuations on a genuine second-order phase transition is applied to the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $β$ regime. Technically this is achieved by a dynamical field-theoretical decoration of MCT that can be studied by a loop expansion. An explicit computation shows that at all orders the leading contributions are the same of a dynamical stochastic glassy equation, {\it i.e} an extension of the standard MCT equation for the critical correlator with local random fluctuations of the…
Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field $h$ are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature $T$. For each process with $(T; \tw, h)$, $\tw$ being the waiting time before the field is switched on, we extract the dynamical crossover time, $\tcr(T; \tw, h)$. We have found a nice scaling relation between the two characteristic length scales which are properly determined from $\tcr$ and $\tw$ and then are normalized by the static field crossover length introduced in the SG dr…
Motivated by the mean field prediction of a Gardner phase transition between a "normal glass" and a "marginally stable glass", we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for colloidal or granular glasses. Deep inside the glass phase, we find that a sharp crossover pressure $P_{\rm G}$ separates two distinct dynamical regimes. For pressure $P < P_{\rm G}$, the glass behaves as a normal solid, displaying fast dynamics that quickly equilibrates within the glass free energy basin. For $P>P_{\rm G}$, instead, the dynamics becomes stro…
We study the non-equilibrium dynamics of the spherical p-spin models in the scaling regime near the plateau and derive the corresponding scaling functions for the correlators. Our main result is that the matching between different time regimes fixes the aging function in the aging regime to $h(t)=\exp(t^{1-μ})$. The exponent $μ$ is related to the one giving the length of the plateau. Interestingly $1-μ$ is quickly very small when one goes away from the dynamic transition temperature in the glassy phase. This gives new light on the interpretation of experiments and simulations where simple agin…
We discuss two main universal dynamic crossovers in a liquid that correspond to relaxation times of 1 ps and 10^{-7}--10^{-6} s. We introduce the concept of liquid elasticity length $d_{\rm el}$. At room temperature, $d_{\rm el}$ is several Åin water and increases to 0.01 mm in honey and 1 mm in tar. We discuss that on temperature decrease, $d_{\rm el}=d_{\rm m}$ and $d_{\rm el}=L$ correspond to the two dynamic crossovers, where $d_{\rm m}$ is the medium-range order and L is system size. The second crossover defines all kinetic aspects of the glass transition whereas ``thermodynamic'' glass tr…
We discuss a novel approach, the point-to-set correlation functions, that allows to determine relevant static and dynamic length scales in glass-forming liquids. We find that static length scales increase monotonically when the temperature is lowered, whereas the measured dynamic length scale shows a maximum around the critical temperature of mode-coupling theory. We show that a similar non-monotonicity is found in the temperature evolution of certain finite size effects in the relaxation dynamics. These two independent sets of results demonstrate the existence of a change in the transport mec…
Motivated by recent experiments of exceptional accuracy, we study numerically the spin-glass dynamics in a film geometry. We cover all the relevant time regimes, from picoseconds to equilibrium, at temperatures at and below the 3D critical point. The dimensional crossover from 3D to 2D dynamics, that starts when the correlation length becomes comparable to the film thickness, consists of four dynamical regimes. Our analysis, based on a Renormalization Group transformation, finds consistent the overall physical picture employed by Orbach et al. in the interpretation of their experiments.
Dynamic scaling analyses are performed in the spin-glass phase of the $\pm J$ Ising, the {\it XY}, and the Heisenberg models in three dimensions. We found a crossover from the critical dynamics to the ground-state dynamics in the Ising model and the Heisenberg model. The ground-state dynamics of the Ising model is characterized by an activation law with a finite energy gap: the typical time diverges exponentially. On the other hand, the typical time in the Heisenberg model diverges algebraically with the inverse temperature. Algebraic relaxation with a finite dynamic exponent is observed after…
Existing theories explain spin glass transition in terms of a phase transition and order parameters, and assume the existence of a distinct spin glass phase. In addition to problems related to clarifying the nature of this phase, the common challenge is to explain profound dynamic effects. Here, we propose that the main experimental results of spin glass transition can be understood in an entirely dynamic picture, without a reference to a distinct spin glass phase, phase transition and order parameters. In this theory, the susceptibility cusp at the glass transition temperature is due to the d…
The shapes of cooperatively rearranging regions in glassy liquids change from being compact at low temperatures to fractal or ``stringy'' as the dynamical crossover temperature from activated to collisional transport is approached from below. We present a quantitative microscopic treatment of this change of morphology within the framework of the random first order transition theory of glasses. We predict a correlation of the ratio of the dynamical crossover temperature to the laboratory glass transition temperature, and the heat capacity discontinuity at the glass transition, Delta C_p. The pr…
Chaotic quantum systems with Lyapunov exponent $λ_\mathrm{L}$ obey an upper bound $λ_\mathrm{L}\leq 2πk_\mathrm{B}T/\hbar$ at temperature $T$, implying a divergence of the bound in the classical limit $\hbar\to 0$. Following this trend, does a quantum system necessarily become `more chaotic' when quantum fluctuations are reduced? Moreover, how do symmetry breaking and associated non-trivial dynamics influence the interplay of quantum mechanics and chaos? We explore these questions by computing $λ_\mathrm{L}(\hbar,T)$ in the quantum spherical $p$-spin glass model, where $\hbar$ can be continuou…
We propose that the properties of glass transition can be understood on the basis of elastic waves. Elastic waves originating from atomic jumps in a liquid propagate local expansion due to the anharmonicity of interatomic potential. This creates dynamic compressive stress, which increases the activation barrier for other events in a liquid. The non-trivial point is that the range of propagation of high-frequency elastic waves, $d_{\rm el}$, increases with liquid relaxation time $τ$. A self-consistent calculation shows that this increase gives the Vogel-Fulcher-Tammann (VFT) law. In the propose…
We study the emergence of a crossover from entropically driven to thermally activated dynamics in different versions of the `entropic' phase space model introduced by Barrat and Mézard, and previously considered in the zero temperature limit. We first focus on the low temperature (T < Tg) aging phase of the original model and show that a short time singularity appears in the correlation function for Tg/2 < T < Tg, leading to dynamical ultrametricity at T=Tg. We then consider the finite size version of this model, showing that the long time dynamics is always thermally activated beyond a size d…
This paper provides an in-depth empirical analysis of several evolutionary algorithms on the one-dimensional spin glass model with power-law interactions. The considered spin glass model provides a mechanism for tuning the effective range of interactions, what makes the problem interesting as an algorithm benchmark. As algorithms, the paper considers the genetic algorithm (GA) with twopoint and uniform crossover, and the hierarchical Bayesian optimization algorithm (hBOA). hBOA is shown to outperform both variants of GA, whereas GA with uniform crossover is shown to perform worst. The differen…
We report measurements of the real and imaginary parts of the AC conductivity in the quantum limit, \hbar ω> k_B T of insulating nominally uncompensated n-type silicon. The observed frequency dependence shows evidence for a crossover from interacting Coulomb glass-like behavior at lower energies to non-interacting Fermi glass-like behavior at higher energies across a broad doping range. The crossover is sharper than predicted and cannot be described by any existing theories. Despite this, the measured crossover energy can be compared to the theoretically predicted Coulomb interaction energy an…
We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass ord…
In stark contrast with the conventional understanding of the glass transition, where the transition from glass to liquid appears as a dynamic process where atoms/molecules cooperatively relax into the equilibrium phase, we experimentally show that the nature of the glass transition depends at a given temperature on the ratio between the relaxation time of the glass, τ_glass, taken as its transformation time, and the alpha relaxation time, τ_α. Although the relaxation of liquid-cooled glasses is not totally synchronous, due to the existence of a distribution of relaxation times, there has been …
The stability of the spin-glass phase against a magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glasses. Effective couplings and effective fields associated with length scale L are measured by a numerical domain-wall renormalization group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H goes to zero but remains finite for any non-zero H, implying that the spin-gla…
Aging phenomena of short-range Ising spin glass models have been investigated using Monte Carlo simulations. It is found that in the low-temperature spin-glass phase the mean domain size exhibits a crossover from a power-law growth associated with the critical fluctuation at the transition temperature to slower growth inherent in the low-temperature phase. The temperature dependence of the growth law of the domain size can be almost explained by this crossover. We also find that the spin-autocorrelation function in the quasi-equilibrium regime follows the expected scaling behavior from the dro…
The behaviour of a model glass forming liquid is analyzed for a range of densities, with a focus on the temperature interval where the liquid begins to display non-Arrhenius temperature dependence of relaxation times. Analyzing the dynamics along with properties of local potential energy minima sampled by the liquid, a crossover or onset temperature $T_s$ is identified below which the liquid manifests {\it slow dynamics}, and a change in the character of typical local potential energy minima.
Non-Monotonic Dynamical Correlations Across The Glass Crossover
Eindhoven University of Technology（埃因霍温理工大学）；Institute for Complex Molecular Systems, Eindhoven University of Technology（埃因霍温理工大学复杂分子系统研究所）；Deutsches Zentrum für Luftund Raumfahrt (DLR)（德国航空航天中心）；Heinrich-Heine-Universität Düsseldorf（杜塞尔多夫大学）；Institute of Complex Systems (ISC) - CNR, Rome unit（罗马复杂系统研究所（国家研究委员会））；Sapienza Università di Roma（罗马第一大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Roma I（意大利国家核物理研究所罗马一分部）
Equilibrium properties of the three-dimensional isotropic Heisenberg spin glass are studied by extensive Monte Carlo simulations, with particular attention to the nature of its phase transition. A finite-size-scaling analysis is performed both for the spin-glass (SG) and the chiral-glass (CG) orders. Our results suggest that the model exhibits the CG long-range order at finite temperatures without accompanying the conventional SG long-range order, in contrast to some of the recent works claiming the simultaneous SG and CG transition. Typical length and time scales which represent a crossover f…
Silica is known as the archetypal strong liquid, exhibiting an Arrhenius viscosity curve with a high glass transition temperature and constant activation energy. However, given the ideally isostatic nature of the silica network, the presence of even a small concentration of defects can lead to a significant decrease in both the glass transition temperature and activation energy for viscous flow. To understand the impact of trace level dopants on the viscosity of silica, we measure the viscosity-temperature curves for seven silica glass samples having different impurities, including four natura…
We study the finite-size behavior of two-dimensional spin-glass models. We consider the +-J model for two different values of the probability of the antiferromagnetic bonds and the model with Gaussian distributed couplings. The analysis of renormalization-group invariant quantities, the overlap susceptibility, and the two-point correlation function confirms that they belong to the same universality class. We analyze in detail the standard finite-size scaling limit in terms of TL^(1/nu) in the +-J model. We find that it holds asymptotically. This result is consistent with the low-temperature cr…
We investigate the dynamics of soft sphere liquids through computer simulations for spatial dimensions from $d =3$ to $8$, over a wide range of temperatures and densities. Employing a scaling of density-temperature dependent relaxation times, we precisely identify the density $ϕ_0$ which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between $ϕ_0$ and the athermal jamming density $ϕ_J$, small in 3 and 4 dimensions, increases with dimension, with $ϕ_0 > ϕ_J$ for $d > 4$. We compare our results with r…
By analyzing the experimental data for various glass-forming liquids and polymers, we find that non-exponentiality $β$ and the relaxation time $τ$ are uniquely related: $\log(τ)$ is an approximately linear function of $1/β$, followed by a crossover to a higher linear slope. We rationalize the observed relationship using a recently developed approach, in which the problem of the glass transition is discussed as the elasticity problem.
We demonstrate that recent experimental data (E. Castel et al J.Phys. Cond. Mat. {\bf 21} (2009), 452201) on tungsten bronze compound (TBC) Ba$_2$Pr$_x$Nd$_{1-x}$FeNb$_4$O$_{15}$ can be well explained in our model predicting a crossover from ferroelectric ($x=0$) to orientational (dipole) glass ($x=1$), rather then relaxor, behavior. We show, that since a "classical" perovskite relaxor like Pb(Mn$_{1/3}$ Nb$_{2/3}$)O$_3$ is never a ferroelectric, the presence of ferroelectric hysteresis loops in TBC shows that this substance actually transits from ferroelectric to orientational glass phase wit…
We perform Monte Carlo simulations of the Ising spin glass at low temperature in three dimensions with a +/-J distribution of couplings. Our results display crossover scaling between T=0 behavior, where the order parameter distribution P(q) becomes trivial for L -> $\infty$, and finite-T behavior, where the non-trivial part of P(q) has a much weaker dependence on the size L, and is possibly size independent.
Optical measurements of the real and imaginary frequency dependent conductivity of uncompensated n-type silicon are reported. The experiments are done in the quantum limit, $ \hbarω> k_{B}T$, across a broad doping range on the insulating side of the Metal-Insulator transition (MIT). The observed low energy linear frequency dependence shows characteristics consistent with theories of a Coulomb glass, but discrepancies exist in the relative magnitudes of the real and imaginary components. At higher energies we observe a crossover to a quadratic frequency dependence that is sharper than expected …
The field-cooled (FC) process on an Ising spin-glass model is investigated by a standard Monte Calro (MC) method on one hand, and the equilibrium magnetization of the same system is evaluated by the exchang MC method on the other hand. The two types of simulation reveal intriguing glassy (nonequilibrium) dynamic properties of the FC magnetization (FCM) of the system. Particularly, the FCM decrease is observed when the FC process is halted at a low temperater, although its value is smaller than the corresponding equilibrium value. We present a comprehensive interpretation of such peculiar pheno…
Replica Field Theory for a Generalized Franz--Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation
We perform molecular dynamics simulations to investigate the effect of a glass preparation on its yielding transition under oscillatory shear. We use swap Monte Carlo to investigate a broad range of glass stabilities from poorly annealed to highly stable systems. We observe a qualitative change in the nature of yielding, which evolves from ductile to brittle as glass stability increases. Our results disentangle the relative role of mechanical and thermal annealing on the mechanical properties of amorphous solids, which is relevant for various experimental situations from the rheology of soft m…
The following properties are in the present literature associated with the behavior of super-cooled glass-forming liquids: faster than exponential growth of the relaxation time, dynamical heterogeneities, growing point-to-set correlation length, crossover from mean field behavior to activated dynamics. In this paper we argue that these properties are also present in a much simpler situation, namely the melting of the bulk of an ordered phase beyond a first order phase transition point. This is a promising path towards a better theoretical, numerical and experimental understanding of the above …
The recently developed pragmatical model of asymmetric double-well potentials with a finite lifetime is applied to nonlinear dielectric data in polar undercooled liquids. The viscous effects from the finite lifetime provide a crossover from the cooperative jumps of many molecules at short times to the motion of statistically independent molecules at long times. The model allows to determine the size of cooperatively rearranging regions from nonlinear ω-data and throws a new light on a known inconsistency between nonlinear ω and 3ω-signals for glycerol and propylene carbonate.
We use X-Ray Photon Correlation Spectroscopy to investigate the structural relaxation process in a metallic glass on the atomic length scale. We report evidence for a dynamical crossover between the supercooled liquid phase and the metastable glassy state, suggesting different origins of the relaxation process across the transition. Furthermore, using different cooling rates we observe a complex hierarchy of dynamic processes characterized by distinct aging regimes. Strong analogies with the aging dynamics of soft glassy materials, such as gels and concentrated colloidal suspensions, point at …
We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the dynamic and static phase transition with exponents (respectively) -1/4 and -1. The two length scales are approximately equal well above the mode coupling transition. Their discrepancy increases rapidly as this transition is approached. We argue that this signals a crossover from mode coupling to activated dynamics.
The crossover from back-and-forth jumps between structural minima to the no-return jumps of the viscous flow is modeled in terms of an ensemble of double-well potentials with a finite decay probability. The ensemble is characterized by the Kohlrausch-exponent $β$ of the time dependence $t^β$ of the response at short times. The model is applied to shear and dielectric data from the literature.
We use large scale computer simulations of a glass-forming liquid in which a fraction c of the particles has been permanently pinned. We find that the relaxation dynamics shows an exponential dependence on c. This result can be rationalized by means of a simple theoretical Ansatz and we discuss its implication for thermodynamic theories for the glass-transition. For intermediate and low temperatures we find that the slowing down of the dynamics due to the pinning saturates and that the cooperativity decreases with increasing c, results which indicate that in glass-forming liquids there is a dy…
We propose that the origin of the Vogel-Fulcher-Tammann law is the increase of the range of elastic interaction between local relaxation events in a liquid. In this picture, we discuss the origin of cooperativity of relaxation, the absence of divergence of relaxation time at a finite temperature and the crossover to a more Arrhenius behaviour at low temperature.
Crossover to Sachdev-Ye-Kitaev criticality in an infinite-range quantum Heisenberg spin glass
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institute of Physics, Johannes Gutenberg University Mainz（约翰内斯·古腾堡美因茨大学物理研究所）；Department of Physics, Harvard University（哈佛大学物理学系）；Center for Computational Quantum Physics, Flatiron Institute（平坦研究所计算量子物理中心）；Department of Physics, State University of New York at Buffalo（纽约州立大学布法罗分校物理学系）
Spin and chirality orderings of a three-dimensional XY spin glass are studied by extensive Monte Carlo simulations. By calculating an appropriately defined spin-overlap distribution function, we show that the finite-temperature chiral-glass transition does not accompany the standard spin-glass order, giving support to the spin-chirality decoupling picture. Critical behavior of the chiral-glass transition turns out to be different from that of the Ising spin glass. The chiral-glass ordered state exhibits a one-step-like peculiar replica-symmetry breaking.
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 dis…
