Here is the first part of the summary of my work on random Ising model using real-space renormalization group (RSRG), also known as a Migdal-Kadanoff one. This approximate renormalization scheme was applied to the analysis thermodynamic properties of the model, and of probabilistic properties of a pair correlator, which is a fluctuating object in disordered systems.
PACS numbers: 02.50.-r, 05.20.-y, 05.70.Fh, 64.60.ae, 75.10.-b, 75.10.Hk, 87.10.+e
Keywords: statistical physics, magnetism, spin glass, neural networks
The field-cooled magnetization (FCM) processes of Ising spin glasses under relatively small fields are investigated by experiment on Fe_{0.55}Mn_{0.45}TiO_3 and by numerical simulation on the three-dimensional Edwards-Anderson model. Both results are explained in a unified manner by means of the droplet picture. In particular, the cusp-like behavior of the FCM is interpreted as evidence, not for an equilibrium phase transition under a finite magnetic field, but for a dynamical (`blocking') transition frequently observed in glassy systems.
Dynamics of spin-glasses subjected to slow continuous changes of working enviroment such as slow changes of temperature or interaction bonds are studied based on scaling arguments and numerical simulations of continuous bond changes. Such perturbations lead to a glassy stationary state where the age or domain size of the system are pinned to macroscopic but finite values due to competition between relaxation and chaos effects (rejuvenation). Flutuation-dissipation relation is also pinned to that of a finite age. The scenario explains the anomalously weak cooling rate dependece of spin glasses.
We study microscopic and macroscopic dynamical properties of a frustrated lattice gas, strictly related to usual spin glasses, showing the violation of Stokes-Einstein law. The glassy behaviors are analyzed and related with experimental results in glass former systems.
We consider the random field Ising model and show rigorously that the spin glass susceptibility at equilibrium is always bounded by the ferromagnetic susceptibility, and therefore that no spin glass phase can be present at equilibrium out of the ferromagnet critical line. When the magnetization is, however, fixed to values smaller than the equilibrium one, a glassy phase can exist, as we show explicitly on the Bethe lattice.
We investigate glassy dynamical properties of one component three-dimensional system of particles interacting via pair repulsive potential by the molecular dynamic simulation in the wide region of densities. The glass state is superfragile and it has high glassforming ability. The glass transition temperature Tg has pronounced minimum at densities where the frustration is maximal.
We numerically study finite-dimensional spin glasses at low and zero temperature, finding evidences for (i) strong time/space heterogeneities, (ii) spontaneous time scale separation and (iii) power law distributions of flipping times. Using zero temperature dynamics we study blocking, clustering and persistence phenomena.
By making use of the Langevin dynamics and its generating functional (GF) formulation the influence of the long-range nature of the interaction on the tendency of the glass formation is systematically investigated. In doing so two types of models is considered: (i) the non-disordered model with a pure repulsive type of interaction and (ii) the model with a randomly distributed strength of interaction (a quenched disordered model). The long-ranged potential of interaction is scaled with a number of particles $N$ in such a way as to enable for GF the saddle-point treatment as well as the systema…
The emergence of glassy behavior of the random field Ising model (RFIM) is investigated using an extended mean-field theory approach. Using this formulation, systematic corrections to the standard Bragg-Williams theory can be incorporated, leading to the appearance of a glassy phase, in agreement with the results of the self-consistent screening theory of Mezard and Young. Our approach makes it also possible to obtain information about the low temperature behavior of this glassy phase. We present results showing that within our mean-field framework, the hysteresis and avalanche behavior of the…
We investigate the ferromagnetic-glassy transitions which separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider the cubic-lattice +-J (Edwards-Anderson) Ising model with bond distribution $P(J) = p δ(J - 1) + (1-p) δ(J + 1)$, and present a numerical Monte Carlo study of the critical behavior along the line that marks the onset of ferromagnetism. The finite-size scaling analysis of the Monte Carlo data shows that the ferromagnetic-glassy transition line is slightly re…
We review recent theoretical progress on glassy dynamics, with special emphasis on the importance and universality of the ``aging regime'', which is relevant to many experimental situations. The three main subjects which we address are: (i) Phenomenological models of aging (coarsening, trap models), (ii) Analytical results for the low-temperature dynamics of mean-field models (corresponding to the mode-coupling equations); and (iii) Simple non-disordered models with glassy dynamics. We discuss the interrelation between these approaches, and also with previous work in the field. Several open pr…
A random matrix approach to glassy physics is introduced. It leads to a class of models which exhibit both, glassy low-temperature phases, and double-- and single-well configurations in their potential energy. The distribution of parameters characterizing the local potential energy configurations can be computed, and differ from those assumed in the standard tunneling model and its variants. Still, low-temperature anomalies characteristic of amorphous systems are reproduced, and we are able to distinguish properties which can be expected to be universal from those which cannot.
Low-frequency vibrations of glassy and crystalline orthoterphenyl are studied by means of neutron scattering. Phonon dispersions are measured along the main axes of a single crystal, and the corresponding longitudinal and transversal sound velocities are obtained. For glassy and polycrystalline samples, a density of vibrational states is determined and cross-checked against other dynamic observables. In the crystal, low-lying zone-boundary modes lead to an excess over the Debye density of states. In the glass, the boson peak is located at even lower frequencies. With increasing temperature, bo…
We report the equivalence of the ``Glassy Potts model'', recently introduced by Marinari et al. and the ``Chiral Potts model'' investigated by Nishimori and Stephen. Both models do not exhibit any spontaneous magnetization at low temperature, differently from the ordinary glass Potts model. The phase transition of the glassy Potts model is easily interpreted as the spin glass transition of the ordinary random Potts model.
For the dynamical glassy transition in the $p$-spin mean field spin glass model a thermodynamic description is given. The often considered marginal states are not the relevant ones for this purpose. This leads to consider a cooling experiment on exponential timescales, where lower states are accessed. The very slow configurational modes are at quasi-equilibrium at an effective temperature. A system independent law is derived that expresses their contribution to the specific heat. $t/t_w$-scaling in the aging regime of two-time quantities is explained.
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…
We introduce a non-disordered lattice spin model, based on the principle of minimizing spin-spin correlations up to a (tunable) distance R. The model can be defined in any spatial dimension D, but already for D=1 and small values of R (e.g. R=5) the model shows the properties of a glassy system: deep and well separated energy minima, very slow relaxation dynamics, aging and non-trivial fluctuation-dissipation ratio.
Glass is an under-cooled liquid that very slowly relaxes towards the equilibrium crystalline state. Its energy balance is ill understood, since it is widely believed that the glassy state cannot be described thermodynamically. However, the classical paradoxes involving the Ehrenfest relations and Prigogine-Defay ratio can be explained when the `effective' or `fictive' temperature of the slow modes is taken as additional system parameter. Having straigtened out the proper picture, it is interesting to reconsider glass from a thermodynamic viewpoint. A shard of glass, kept at fixed temperature a…
Monte Carlo studies of the 3D random field $XY$ model on simple cubic lattices of size $64^3$, using two different isotropic random-field probability distributions of moderate strength, show a glassy freezing behavior above $T_c$, and long-range order below $T_c$, consistent with our earlier results for weaker and stronger random fields. This model should describe random pinning in vortex lattices in type-II superconducting alloys, charge-density wave materials, and decagonal quasicrystals.
We have analyzed a non-randomly frustrated spin model which exhibits behavior remarkably similar to the phenomenology of structural glasses. The high-temperature disordered phase undergoes a strong first-order transition to a long-range ordered structure. Using Monte Carlo simulations, we have studied the behavior of the supercooled state by quenching to temperatures below this transition temperature. For a range of supercooling, the system remains ergodic and exhibits dynamics characteristic of supercooled liquids. Below a certain characteristic temperature, however, the system freezes into a…
We investigate the zero-temperature glassy transitions in the square-lattice +- J Ising model, with bond distribution $P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)$; p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5, which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p=0.89, and at p=1/2. Their comparison provides a strong evidence that the glassy critical behavior that occurs for $1-p_0<p<p_0$, $p_0=0.897$, i…
Recent work has suggested the existence of glassy behavior in a ferromagnetic model with a four-spin interaction. Motivated by these findings, we have studied the dynamics of this model using Monte Carlo simulations with particular attention being paid to two-time quantities. We find that the system shares many features in common with glass forming liquids. In particular, the model exhibits: (i) a very long-lived metastable state, (ii) autocorrelation functions that show stretched exponential relaxation, (iii) a non-equilibrium timescale that appears to diverge at a well defined temperature, a…
The existence of an equilibrium glassy phase for charges in a disordered potential with long-range electrostatic interactions has remained controversial for many years. Here we conduct an extensive numerical study of the disorder-temperature phase diagram of the three-dimensional Coulomb glass model using population annealing Monte Carlo to thermalize the system down to extremely low temperatures. Our results strongly suggest that, in addition to a charge order phase, a transition to a glassy phase can be observed, consistent with previous analytical and experimental studies.
The escape of energy injected into one site in a disordered chain of nonlinear oscillators is examined numerically. When the disorder has a `fractal' pattern, the decay of the residual energy at the injection site can be fit to a stretched exponential with an exponent that varies continuously with the control parameter. At low temperature, we see evidence that energy can be trapped for an infinte time at the original site, i.e. classical many body localization.
We numerically study a disordered model for the RNA secondary structure and we find that it undergoes a phase transition, with a breaking of the replica symmetry in the low temperature region (like in spin glasses). Our results are based on the exact evaluation of the partition function.
We consider the zero-temperature dynamics for the infinite-range, non translation invariant one-dimensional spin model introduced by Marinari, Parisi and Ritort to generate glassy behaviour out of a deterministic interaction. It is shown that there can be a large number of metatastable (i.e., one-flip stable) states with very small overlap with the ground state but very close in energy to it, and that their total number increases exponentially with the size of the system.
We present a theoretical discussion of the reversible parking problem, which appears to be one of the simplest systems exhibiting glassy behavior. The existence of slow relaxation, nontrivial fluctuations, and an annealing effect can all be understood by recognizing that two different time scales are present in the problem. One of these scales corresponds to the fast filling of existing voids, the other is associated with collective processes that overcome partial ergodicity breaking. The results of the theory are in a good agreement with simulation data; they provide a simple qualitative pict…
We review 15 years of theoretical and experimental work on the non-linear response of glassy systems. We argue that an anomalous growth of the peak value of non-linear susceptibilities is a signature of growing "amorphous order" in the system, with spin-glasses as a case in point. Experimental results on supercooled liquids are fully compatible with the RFOT prediction of compact "glassites" of increasing volume as temperature is decreased, or as the system ages. We clarify why such a behaviour is hard to explain within purely kinetic theories of glass formation, despite recent claims to the c…
In the present investigation the glass forming ability of Ce65Al25Co10 metallic glass has been reported. It was successfully synthesised using melt spinning techniques. The existence of amorphous phase in Ce65Al25Co10 alloy have been proved using X-ray diffraction (XRD) and transmission electron microscopy (TEM) measurements. The thermal analysis of the synthesised sample using differential scanning calorimetry (DSC) shows a glass transition around 371 K, thus confirms existence of glassy phase at room temperature. The hardness of the synthesised sample at different load have been demonstrated…
Vitrification in colloidal systems typically occurs at high densities driven by sharply varying, short-ranged interactions. The possibility of glassy behavior arising from smoothly varying, long-ranged particle interactions has received relatively little attention. Here we investigate the behavior of screened charged particles, and explicitly demonstrate that these systems exhibit glassy properties in the regime of low temperature and low density. Properties close to this low density (Wigner) glass transition share many features with their hard-sphere counterparts, but differ in quantitative a…
Studies of low-frequency resistance noise demonstrate that glassy freezing occurs in a two-dimensional electron system in silicon in the vicinity of the metal-insulator transition (MIT). The width of the metallic glass phase, which separates the 2D metal and the (glassy) insulator, depends strongly on disorder, becoming extremely small in high-mobility (low-disorder) samples. The glass transition is manifested by a sudden and dramatic slowing down of the electron dynamics, and by a very abrupt change to the sort of statistics characteristic of complicated multistate systems. In particular, the…
Based on experimental evidences we present a phenomenological description of the thermal glass transition as a dynamical phase transition. Different susceptibilities calculated on the basis of this description are in good qualitative agreement with experimental data. As an essential feature this novel view of the glass transition reflects the kinetic as well as the transition aspect of the thermal glass transition.
We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical glassy systems. For our purposes, we specify the Markov stochastic process considered by S. Albeverio and W. Karwowski. As a result we have obtained a random walk on p-adic integer numbers, which provide the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.
Our model of shaken sand, presented in earlier work, has been extended to include a more realistic `glassy' state, i.e., when the sandbox is shaken at very low intensities of vibration. We revisit some of our earlier results, and compare them with our new results on the revised model. Our analysis of the glassy dynamics in our model shows that a variety of ground states is obtained; these fall in two categories, which we argue are representative of regular and irregular packings.
The temperature dependence of the non-ergodicity factor of vitreous GeO$_2$, $f_{q}(T)$, as deduced from elastic and quasi-elastic neutron scattering experiments, is analyzed. The data are collected in a wide range of temperatures from the glassy phase, up to the glass transition temperature, and well above into the undercooled liquid state. Notwithstanding the investigated system is classified as prototype of strong glass, it is found that the temperature- and the $q$-behavior of $f_{q}(T)$ follow some of the predictions of Mode Coupling Theory. The experimental data support the hypothesis of…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I will show how these models can be solved due their mean field properties. Finally, in the last section, I will discuss the difficulties in the generalization of these findings to short range models.
In these lectures I will study some properties that are shared by many glassy systems. I will shown how some of these properties can be understood in the framework of the mean field approach based on the replica method and I will discuss which are the difficulties which we have to face when we apply the replica method to realistic short range models. We finally present a partially successfully application of the replica method to soft sphere glasses.
We consider a frustrated spin model with a glassy dynamics characterized by a slow component and a fast component in the relaxation process. The slow process involves variables with critical behavior at finite temperature T_p and has a global character like the (structural) alpha-relaxation of glasses. The fast process has a more local character and can be associated to the beta-relaxation of glasses. At temperature T>T_p the fast relaxation follows the non-Arrhenius behavior of the slow variables. At T ~< T_p the fast variables have an Arrhenius behavior, resembling the alpha-beta bifurcation…
Motivated by recent experimental results on glassy polymer nanoparticles, we develop a minimal theoretical framework for the glass transition in spherical confinement. This is accomplished using our cooperative-string model for supercooled dynamics, that was successful at recovering the bulk phenomenology and describing the thin-film anomalies. In particular, we obtain predictions for the mobile-layer thickness as a function of temperature, and for the effective glass-transition temperature as a function of the radius of the spherical nanoparticle - including the existence of a critical partic…
Particle swaps can drastically accelerate dynamics in glass. The mechanism is expected to be vital for a fundamental understanding of glassy dynamics. To extract defining features, we propose a partial swappability with a fraction {ϕ_s} of swap-initiating particles, which can only swap locally with each other or with regular particles. We focus on the swap-dominating regime. At all temperatures studied, particle diffusion coefficients scale with {ϕ_s} in unexpected power laws with temperature-dependent exponents, consistent with the kinetic picture of glass transition. At small {ϕ_s}, swap-ini…
We consider the adiabatic evolution of glassy states under external perturbations. Although the formalism we use is very general, we focus here on infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e. compression or (volume preserving) shear-strain, and we compute the response of glassy states to such perturbations: pressure and shear-stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. F…
We present a study of orientational relaxation dynamics in thin films of a low-molecular-weight glass-former as a function of temperature and film thickness. The relaxation is probed by second-harmonic generation after release of a poling electric field. From the measured decays of the second-harmonic signal and their fitting with a stretched exponential, we can determine the distribution of relaxation times in the system. As temperature decreases from above the glass transition, we observe that the width of the distribution first increases under confinement, but that deeper in the glassy stat…
In this talk I review some recent developments which shed light on the main connections between structural glasses and mean-field spin glass models with a discontinuous transition. I also discuss the role of quantum fluctuations on the dynamical instability found in mean-field spin glasses with a discontinuous transition. In mean-field models with pairwise interactions in a transverse field it is shown, in the framework of the static approximation, that such instability is suppressed at zero temperature.
We review the search for the glass transition in water in its various amorphous forms, and highlight the paradoxes that the search has produced. Focussing on the glassy form of water obtained by hyperquenching, we examine its reported calorimetric properties in the light of new findings for bulk glassformers vitrified by hyperquenching. Like the hyperquenched bulk glassformers, hyperquenched water exhibits a large relaxation exotherm on reheating, as the high enthalpy quenched form relaxes to a lower enthalpy state. When the scanning temperature is scaled by the glass transition temperature, t…
We present a detailed study of the electronic transport properties on a single crystalline specimen of the moderately disordered heavy fermion system URh$_2$Ge$_2$. For this material, we find glassy electronic transport in a single crystalline compound. We derive the temperature dependence of the electrical conductivity and establish metallicity by means of optical conductivity and Hall effect measurements. The overall behavior of the electronic transport properties closely resembles that of metallic glasses, with at low temperatures an additional minor spin disorder contribution. We argue tha…
The state-following technique allows the study of metastable glassy states under external perturbations. Here we show how this construction can be used to study the behavior of glassy states of Hard Spheres in infinite dimensions under compression or shear strain. In a preceding work it has been shown that in both cases, when the external perturbation is sufficiently strong, glassy states undergo a second-order transition, called the Gardner transition, whereupon a hierarchical structure of marginal micro-states manifests within the original glass state. The purpose of this work is to study th…
Upon cooling, glass-forming liquids experience a two-step relaxation associated to the cage rattling and the escape from the cage, and the following decoupling between the \b{eta}- and the α-relaxations. The found decoupling behaviors have greatly changed the face of glassy physics and materials studies. Here we report a novel dynamic decoupling that the relaxation function changes gradually from a single-step to a two-step form as temperature declines through the stress relaxation of various metallic glasses in a broad time and temperature range below glass transition temperature (Tg). Such a…
Erratum to Phys. Rev. X 4, 021008 (2014): The critical exponent associated with the ferromagnetic susceptibility was computed incorrectly. Furthermore, Ising ferromagnets on the Chimera topology have the same universality class as two-dimensional Ising ferromagnets.
Dynamics of classical Heisenberg spins, ${\bf S}_i=({\bf s}_i,S_{iz})$, on the Kagomé lattice has been studied. An ideal Heisenberg Kagomé antiferromagnet is known to remain disordered down to T=0 due to the macroscopic degeneracy of the ground state. Through the study, however, we find that ${\bf S}_i$ and their planar components ${\bf s}_i$ behave in a qualitatively different way and especially planar spins (${\bf s}_i$) show the exotic glass-like transition in the very low temperature $T\sim 0.003J$ ($J$: spin exchange). The glassy behaviors of ${\bf s}_i$ would be found to be driven by the…
