Recent ideas based on the properties of assemblies of frictionless particles in mechanical equilibrium provide a perspective of amorphous systems different from that offered by the traditional approach originating in liquid theory. The relation, if any, between these two points of view, and the relevance of the former to the glass phase, has been difficult to ascertain. In this paper we introduce a model for which both theories apply strictly: it exhibits on the one hand an ideal glass transition and on the other `jamming' features (fragility, soft modes) virtually identical to that of real systems. This allows us to disentangle the different contents and domains of applicability of the two physical phenomena.
The Frenkel Kontorova (FK) model is known to exhibit the so called Aubry's transition which is a jamming or frictional transition at zero temperature. Recently we found similar transition at zero and finite temperatures in a super-conducting Josephson junction array (JJA) on a square lattice under external magnetic field. In the present paper we discuss how these problems are related.
We investigate the glass and the jamming transitions of hard spheres in finite dimensions $d$, through a revised cell theory, that combines the free volume and the Random First Order Theory (RFOT). Recent results show that in infinite dimension the ideal glass transition and jamming transitions are distinct, while based on our theory we argue that they indeed coincide for finite $d$. As a consequence, jamming results into a percolation transition described by RFOT, with a static length diverging with exponent $ν=2/d$, which we verify through finite size scaling, and standard critical exponents…
The shear rheology of soft particles systems becomes complex at large density because crowding effects may induce a glass transition for Brownian particles, or a jamming transition for non-Brownian systems. Here we successfully explore the hypothesis that the shear stress contributions from glass and jamming physics are `additive'. We show that the experimental flow curves measured in a large variety of soft materials (colloidal hard spheres, microgel suspensions, emulsions, aqueous foams) as well as numerical flow curves obtained for soft repulsive particles in both thermal and athermal limit…
We discuss the analytical solution through the cavity method of a mean field model that displays at the same time an ideal glass transition and a set of jamming points. We establish the equations describing this system, and we discuss some approximate analytical solutions and a numerical strategy to solve them exactly. We compare these methods and we get insight into the reliability of the theory for the description of finite dimensional hard spheres.
We investigate the statistical mechanics of glass-forming materials and jamming matter by means of a geometrically driven approach based on a revised cell theory. By considering the system as constituted of jammed blocks of increasing sizes, we obtain a unified picture that describes accurately the whole process from low densities to limit densities at the glass/jamming transition. The approach retrieves many of the aspects of existing theories unifying them into a coherent framework. In particular, at low densities we find a free volume regime, based on local relaxation process, at intermedia…
We present the study of the landscape structure of athermal soft spheres both as a function of the packing fraction and of the energy. We find that, on approaching the jamming transition, the number of different configurations available to the system has a steep increase and that a hierarchical organization of the landscape emerges. We use the knowledge of the structure of the landscape to predict the values of thermodynamic observables on the edge of the transition.
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…
We construct and analyze a family of $M$-component vectorial spin systems which exhibit glass transitions and jamming within supercooled paramagnetic states without quenched disorder. Our system is defined on lattices with connectivity $c=αM$ and becomes exactly solvable in the limit of large number of components $M \to \infty$. We consider generic $p$-body interactions between the vectorial Ising/continuous spins with linear/non-linear potentials. The existence of self-generated randomness is demonstrated by showing that the random energy model is recovered from a $M$-component ferromagnetic …
Amorphous solids, such as glasses, have complex responses to deformations, with significant consequences in material design and applications. In this respect two intertwined aspects are important: stability and reversibility. It is crucial to understand on the one hand how a glass may become unstable due to increased plasticity under shear deformations; on the other hand, to what extent the response is reversible, meaning how much a system is able to recover the original configuration once the perturbation is released. Here we focus on assemblies of hard spheres as the simplest model of amorph…
We study the glass and jamming transition of finite-dimensional models of simple liquids: hard- spheres, harmonic spheres and more generally bounded pair potentials that modelize frictionless spheres in interaction. At finite temperature, we study their glassy dynamics via field-theoretic methods by resorting to a mapping towards an effective quantum mechanical evolution, and show that such an approach resolves several technical problems encountered with previous attempts. We then study the static, mean-field version of their glass transition via replica theory, and set up an expansion in term…
While the glass transition at non-zero temperature seems to be hard to access for experimental, theoretical, or simulation studies, jamming at zero temperature has been explored in great detail. It is a widely discussed question whether this athermal jamming transition is related to the glass transition. Motivated by the exploration of the energy landscape that has been successfully used to describe athermal jamming, we introduce a new method to determine whether the configuration space of a soft sphere system can be explored within a reasonable timescale or not, i.e., whether the system is er…
We discuss the linear and non-linear rheology of concentrated (sub)microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from…
Anomalous Criticality of Absorbing State Transition toward Jamming
National Laboratory of Solid State Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室）；Collaborative Innovation Center of Advanced Microstructures and School of Physics, Nanjing University（南京大学先进微结构协同创新中心及物理学院）
Glasses are amorphous solids whose constituent particles are caged by their neighbors and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a "roughness transition" to fractal basins. This brings about isostaticity at jamming and marginality of glassy states near jamming. Critical exponents for the basin width, the weak force distribution, and the spat…
Studying the jamming transition of granular and colloidal systems, has lead to a proliferation of theoretical and numerical results formulated in the language of the eigenspectrum of the dynamical matrix for these disordered system. Only recently however, these modes have been accessed experimentally in colloidal and granular media, computing the eigenmodes of the covariance matrix of the particle positions. At the same time new conceptual and methodological questions have appeared, regarding the interpretation of these results. In the present paper, we first give an overview of the theoretica…
Marginally stable solids have peculiar physical properties that were discovered and analyzed in the context of the jamming transition. We theoretically investigate the existence of marginal stability in a prototypical model for structural glass-formers, combining analytical calculations in infinite dimensions to computer simulations in three dimensions. While mean-field theory predicts the existence of a Gardner phase transition towards a marginally stable glass phase at low temperatures, simulations show no hint of diverging timescales or lengthscales, but reveal instead the presence of spars…
On the universality of jamming percolation: reply to the comment of Jeng and Schwarz
In Phys. Rev. Lett. 96，035702（2006）中，我们介绍了一类显示动态玻璃化转变的动力学约束模型。我们集中讨论了一个特殊的例子：“骑士”模型。正如Jeng和Schwarz cond-mat/0612484正确指出的那样，我们忽略了骑士模型的一些额外的定向冻结结构，这些结构不是简单的定向渗流（DP）路径：这些“更厚”的定向结构降低了临界密度。在这里，我们认为，尽管如此，全定向过程是在DP普适性类和T-结之间的垂直段这些引起了干扰渗流过渡与我们以前的工作中讨论的普遍性质。此外，我们提出了其他模型，我们以前的所有结果，包括临界密度的值，严格举行。
We compute the shear modulus of amorphous hard and soft spheres, using the exact solution in infinite spatial dimensions that has been developed recently. We characterize the behavior of this observable in the whole phase diagram, and in particular around the glass and jamming transitions. Our results are consistent with other theoretical approaches, that are unified within this general picture, and they are also consistent with numerical and experimental results. Furthermore, we discuss some properties of the out-of-equilibrium dynamics after a deep quench close to the jamming transition, and…
We review the physics of jamming from the theoretical, experimental and numerical perspectives. We summarize the mean-field theory of jamming and the marginally stable solid phase, with particular emphasis on the connection with the Replica Symmetry Breaking theory of glasses. We report validations of the mean-field theory of jamming from experimental and numerical studies of critical behaviors near the transition. In particular, we describe the physics of jamming of frictionless, spherical particles, as well as more recent work on jamming of frictionless, non-spherical particles and frictiona…
Via molecular dynamics simulations, we unveil the hysteretic nature of the jamming transition of soft repulsive frictionless spheres, as it occurs varying the volume fraction or the shear stress. In a given range of control parameters the system may be found both in a flowing and in an jammed state, depending on the preparation protocol. The hysteresis is due to an underlying energy landscape with many minima, as explained by a simple model, and disappears in the presence of strong viscous forces and in the small $σ$ limit. In this limit, structural quantities are continuous at the transition,…
A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction $ϕ_\text{J}$ of the polydisperse system as a simple function of $M_1M_3/M_2^2$, where $M_k$ is the $k$th moment of the size distribution. An analysis of experimental and simulation data of $ϕ_\text{J}$ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mi…
We develop a microscopic theory to analyze the phase behaviour and compute correlation functions of dense assemblies of soft repulsive particles both at finite temperature, as in colloidal materials, and at vanishing temperature, a situation relevant for granular materials and emulsions. We use a mean-field statistical mechanical approach which combines elements of liquid state theory to replica calculations to obtain quantitative predictions for the location of phase boundaries, macroscopic thermodynamic properties and microstructure of the system. We focus in particular on the derivation of …
We introduce a new model of hard spheres under confinement for the study of the glass and jamming transitions. The model is an one-dimensional chain of the $d$-dimensional boxes each of which contains the same number of hard spheres, and the particles in the boxes of the ends of the chain are quenched at their equilibrium positions. We focus on the infinite dimensional limit ($d \to \infty$) of the model and analytically compute the glass transition densities using the replica liquid theory. From the chain length dependence of the transition densities, we extract the characteristic length scal…
Dynamics of structural models with a long-range interaction: glassy versus non-glassy behavior
利用Langevin动力学及其生成泛函（GF）公式，系统地研究了相互作用的长程性质对玻璃形成趋势的影响。在这样做时，考虑两种类型的模型：（i）具有纯排斥型相互作用的非无序模型和（ii）具有随机分布的相互作用强度的模型（淬火无序模型）。长程相互作用势与粒子数$N$成比例，使得GF的鞍点处理以及系统的1/N - expansion around it. We表明，非无序模型没有玻璃化转变，这与模耦合理论（MCT）预测的平均场极限一致。另一方面，具有长程相互作用的模型，其上具有淬火无序，导致MC -方程，其对于$p$ -自旋玻璃模型和随机介质中的聚合物歧管是通用的。
In this Letter, we analyze the quantum dynamics of the perceptron model: a particle is constrained on a $N$-dimensional sphere, with $N\to \infty$, and subjected to a set of randomly placed hard-wall potentials. This model has several applications, ranging from learning protocols to the effective description of the dynamics of an ensemble of infinite-dimensional hard spheres in Euclidean space. We find that the jamming transition with quantum dynamics shows critical exponents different from the classical case. We also find that the quantum jamming transition, unlike the typical quantum critica…
We discuss an Ising spin glass where each $S=1/2$ spin is coupled antiferromagnetically to three other spins (3-regular graphs). Inducing quantum fluctuations by a time-dependent transverse field, we use out-of-equilibrium quantum Monte Carlo simulations to study dynamic scaling at the quantum glass transition. Comparing the dynamic exponent and other critical exponents with those of the classical (temperature-driven) transition, we conclude that quantum annealing is less efficient than classical simulated annealing in bringing the system into the glass phase. Quantum computing based on the qu…
Typical versus average helicity modulus in the three-dimensional gauge glass: Understanding the vortex glass phase
我们用蒙特卡罗模拟数值计算了三维规玻璃的螺旋度模量。由于平均自由能是独立的扭转角，它是预期的平均螺旋度模量，直接相关的超流密度，消失时进行模拟与周期性的边界条件。对于非零的典型（中值）值，情况不一定如此，因为螺旋度模量在不同无序实现中的分布是非常不对称的。我们表明，螺旋度模量分布的数据很好地描述了一个广义极值分布与非零的位置参数（最可能的值）。位置参数的有限尺寸标度分析产生与以前的结果一致的临界温度和临界指数。这表明位置参数是一个很好的可观测量。关于超流密度是否在涡旋玻璃相中消失，存在着相互矛盾的说法，Fisher等人[Phys. Rev. B 43，130（1991）]认为它是有限的，而Korshunov [Phys. Rev. B 63，174 - 514（2001）]预测它是零。由于规范玻璃常被用来描述高温超导体中的涡旋玻璃，我们根据我们在规范玻璃上的结果讨论了这个问题。
We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular emphasis on spatially heterogeneous dynamics. We review the main theoretical approaches currently available to account for these glassy phenomena, including recent developments regarding mean-field theory of liquids and glasses, novel computational tools, and connections to the jamming transition. Finally, the physics of aging and off-equilibrium dynamics e…
Glasses prepared by physical vapour deposition have been shown to be remarkably more stable than those prepared by standard cooling protocols, with properties that appear to be similar to systems aged for extremely long times. When subjected to a rapid rise in temperature, ultrastable glasses anneal towards the liquid in a qualitatively different manner than ordinary glasses, with the seeming competition of different timescales and lengthscales. We numerically reproduce the phenomenology of ultrastable glass annealing with a kinetically constrained model, a three dimensional East model with so…
The jamming scenario of disordered media, formulated about 10 years ago, has in recent years been advanced by analyzing model systems of granular media. This has led to various new concepts that are increasingly being explored in in a variety of systems. This chapter contains an introductory review of these recent developments and provides an outlook on their applicability to different physical systems and on future directions. The first part of the paper is devoted to an overview of the findings for model systems of frictionless spheres, focussing on the excess of low-frequency modes as the j…
