Paper | Original Paper


*Yuliang Jin, Hajime Yoshino,
Exploring the complex free energy landscape of the simplest glass by rheology,
Nature Communications 8, 14935 (2017).

[Summary] For amorphous solids, it has been intensely debated whether the traditional view on solids, in terms of the ground state and harmonic low energy excitations on top of it, such as phonons, is still valid. Recent theoretical developments of amorphous solids revealed the possibility of unexpectedly complex free energy landscapes where the simple harmonic picture breaks down. Here we demonstrate that standard rheo- logical techniques can be used as powerful tools to examine non-trivial consequences of such complex free energy landscapes. By extensive numerical simulations on a hard sphere glass under quasi-static shear at finite temperatures, we show that, above the so-called Gardner transition density, the elasticity breaks down, the stress relax- ation exhibits slow and aging dynamics, and the apparent shear modulus becomes protocol-dependent. Being designed to be reproducible in laboratories, our approach may trigger explorations of the complex free energy landscapes of a large variety of amorphous materials.

Harukuni Ikeda, Kunimasa Miyazaki and *Giulio Biroli,
The Fredrickson-Anderson model with random pinning on Bethe lattices and its MCT transitions,
EPL 116, 56004/1-8 (2017).

[Summary] We investigate the dynamics of the randomly pinned Fredrickson-Andersen modelon the Bethe lattice. We find a line of random pinning dynamical transitions whose dynamicalcritical properties are in the same universality class of the A2 and A3 transitions of the modecoupling theory. The A3 behavior appears at the terminal point, where the relaxation becomeslogarithmic and the relaxation time diverges exponentially. We explain the critical behavior in terms of self-induced disorder and avalanches, strengthening the relationship discussed in recent works between glassy dynamics and random field Ising model.


*Harukuni Ikeda, Kunimasa Miyazaki, and *Atsushi Ikeda,
A note on the replica liquid theory of binary mixtures,
Journal of Chemical Physics 145, 216101/1-2 (2016).

[Summary] We reformulate the Replica Liquid Theory in order to resolve the inherent problem related to the configurational entropy of the supercooled binary systems near the glass transition. By rewriting generating functions using the Morita-Hiroike representation, we have shown that the configurational entropy correctly converges to that of monatomic system in this limit.

Ryoji Miyazaki, Takeshi Kawasaki, and *Kunimasa Miyazaki,
Cluster Glass Transition of Ultrasoft-Potential Fluids at High Density,
Physical Review Letterrs 117, 165701/1-5 (2016).

[Summary] Using molecular dynamics simulation, we investigate the slow dynamics of a supercooled binarymixture of soft particles interacting with a generalized Hertzian potential. At low density, it displays typicalslow dynamics near its glass transition temperature. At higher densities, particles bond together, formingclusters, and the clusters undergo the glass transition. The number of particles in a cluster increases one byone as the density increases. We demonstrate that there exist multiple cluster-glass phases characterized bya different number of particles per cluster, each of which is separated by distinct minima. Surprisingly, a socalledhigher order singularity of the mode-coupling theory signaled by a logarithmic relaxation is observedin the vicinity of the boundaries between monomer and cluster glass phases. The system also exhibits richand anomalous dynamics in the cluster glass phases, such as the decoupling of the self- and collectivedynamics.

Daijyu Nakayama, Hajime Yoshino, Francesco Zamponi,
Protocol-dependent shear modulus of amorphous solids,
Journal of Statistical Mechanics: Theory and Experiment 10, 104001 (2016).

We investigate the linear elastic response of amorphous solids to a shear strain at zero temperature. We find that the response is characterized by at least two distinct shear moduli. The first one, πZFC, is associated with the linear response of a single energy minimum. The second, πFC, is related to sampling, through plastic events, an ensemble of distinct energy minima. We provide examples of protocols that allow one to measure both shear moduli. In agreement with a theoretical prediction based on the exact solution in infinite spatial dimensions, the ratio πFC/πZFC is found to vanish proportionally to the square root of pressure at the jamming transition. Our results establish that amorphous solids are characterized by a rugged energy landscape, which has a deep impact on their elastic response, as suggested by the infinite-dimensional solution.

Misaki Ozawa, Kang Kim, *Kunimasa Miyazaki,
Tuning Pairwise Potential Can Control the Fragility of Glass-Forming Liquids: From Tetrahedral Network to Isotropic Soft Sphere Models,
Journal of Statistical Mechanics: Theory and Experiment None, 074002/1-21 (2016).

[Summary] We perform molecular dynamics simulations for a SiO2 glass formermodel proposed by Coslovich and Pastore (CP) over a wide range of densities. Thedensity variation can be mapped onto the change of the potential depth between Siand O interactions of the CP model. By reducing the potential depth (or increasingthe density), the anisotropic tetrahedral network structure observed in the originalCP model transforms into the isotropic structure with the purely repulsive softspherepotential. Correspondingly, the temperature dependence of the relaxationtime exhibits the crossover from Arrhenius to super-Arrhenius behavior. Beingable to control the fragility over a wide range by tuning the potential of a singlemodel system helps us to bridge the gap between the network and isotropic glassformers and to obtain the insight into the underlying mechanism of the fragility. We study the relationship between the fragility and dynamical properties such as the magnitude of the Stokes–Einstein violation and the stretch exponent in the density correlation function. We also demonstrate that the peak of the specific heat systematically shifts as the density increases, hinting that the fragility is correlated with the hidden thermodynamic anomalies of the system.

Daniele Coslovich, *Atsushi Ikeda, Kunimasa Miyazaki,
Mean-field dynamic criticality and geometric transition in the Gaussian core model,
Physical Review E 93, 042602/1-8 (2016).

[Summary] We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.


Harukuni Ikeda, *Kunimasa Miyazaki,
Facilitated spin model on Bethe lattice with random pinning,
EPL 112, 16001 (2015).

[Summary] We study the effects of random pinning on the Fredrickson-Andersen model on the Bethe lattice. We find that the nonergodic transition temperature rises as the fraction of the pinned spins increases and the transition line terminates at a critical point. The freezing behavior of the spins is analogous to that of a randomly pinned p-spin mean-field spin glass model which has been recently reported. The diverging behavior of correlation lengths in the vicinity of the terminal critical point is found to be identical to the prediction of the inhomogeneous mode-coupling theory at the A 3 singularity point for the glass transition.

Misaki Ozawa, *Walter Kob, Atsushi Ikeda, Kunimasa Miyazaki,
Reply to Chakrabarty et al.: Particles move even in ideal glasses,
Proceedings of the National Academy of Sciences of the United States of America 112, E4821-E4822 (2015).

[Summary] In their letter, Chakrabarty et al. (1) point out that their data on the relaxation dynamics are inconsistent with the thermodynamic data presented in our paper (2). They argue that from their results and the predictions of the random first-order transition theory (3) one must conclude that our configurational entropy $S_c$ is “quantitatively not accurate.” In the following we will show that this conclusion is not necessarily valid.

Misaki Ozawa, *Walter Kob, Atsushi Ikeda, and Kunimasa Miyazaki,
Equilibrium phase diagram of a randomly pinned glass-former,
Proceedings of the National Academy of Sciences of the United States of America 112, 6914-6919 (2015).

[Summary] Confirming by experiments or simulations whether or not an ideal glass transition really exists is a daunting task, because at this point the equilibration time becomes astronomically large. Recently it has been proposed that this difficulty can be bypassed by pinning a fraction of the particles in the glass-forming system. Here we study numerically a liquid with such random pinned particles and identify the ideal glass transition point TK at which the configurational entropy vanishes, thus realizing for the first time, to our knowledge, a glass with zero entropy. We find that as the fraction of pinned particles increases, the TK line crosses the dynamical transition line, implying the existence of an end point at which theory predicts a new type of criticality.

Corrado Rainone, Pierfrancesco Urbani, Hajime Yoshino, *Francesco Zamponi,
Following the evolution of glassy states under external perturbations: compression and shear-strain,
Physical Review Letters 114, 015701/1-5 (2015).

[Summary] We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for 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. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.


Saroj Kumar Nandi, *Giulio Biroli, Jean-Philippe Bouchaud, Kunimasa Miyazaki, and David R. Reichman,
Critical dynamical heterogeneities close to continuous second-order glass transitions,
Physical Review Letters 113, 245701/1-5 (2014).

[Summary] We analyze, using inhomogeneous mode-coupling theory, the critical scaling behavior of the dynamical susceptibility at a distance ε from continuous second-order glass transitions. We find that the dynamical correlation length ξ behaves generically as ε−1/3 and that the upper critical dimension is equal to six. More surprisingly, we find that ξ grows with time as ln2t exactly at criticality. All of these results suggest a deep analogy between the glassy behavior of attractive colloids or randomly pinned supercooled liquids and that of the random field Ising model.

Hajime Yoshino and Francesco Zamponi,
The shear modulus of glasses: results from the full replica symmetry breaking solution,
Physical Review E 90, 022302/1-14 (2014).

[Summary] 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, which 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 show that a combined measure of the shear modulus and of the mean square displacement allows one to probe experimentally the complex structure of phase space predicted by the full replica-symmetry-breaking solution.

Takeshi Kuroiwa and *Kunimasa Miyazaki,
Brownian motion with multiplicative noises revisited,
Journal of Physics A: Mathematical and Theoretical 47, 012001/1-8 (2014).

[Summary] The Langevin equation with multiplicative noise and a state-dependent transport coefficient should always complemented with the proper interpretation rule of the noise, such as the Itˆo and Stratonovich conventions. Although the mathematical relationship between the different rules and how to translate from one rule to another are well established, the subject of which is amore physically natural rule still remains controversial. In this communication, we derive the overdamped Langevin equation with multiplicative noise for Brownian particles, by systematically eliminating the fast degrees of freedomof the underdamped Langevin equation. The Langevin equations obtained here vary depending on the choice of the noise conventions but they are different representations for an identical phenomenon. The results apply to multivariable, nonequilibrium, non-stationary systems, and other general settings.


*Kang Kim, Shinji Saito, Kunimasa Miyazaki, Giulio Biroli, and *David R. Reichman,
Dynamic Length Scales in Glass-Forming Liquids: An Inhomogeneous Molecular Dynamics Simulation Approach,
The Journal of Physical Chemistry B 117, 13259–13267 (2013).

[Summary] In this work, we numerically investigate a new method for the characterization of growing length scales associated with spatially heterogeneous dynamics of glass-forming liquids. This approach, motivated by the formulation of the inhomogeneous mode-coupling theory (IMCT) [Biroli, G.; et al. Phys. Rev. Lett. 2006 97, 195701], utilizes inhomogeneous molecular dynamics simulations in which the system is perturbed by a spatially modulated external potential. We show that the response of the two-point correlation function to the external field allows one to probe dynamic correlations. We examine the critical properties shown by this function, in particular, the associated dynamic correlation length, that is found to be comparable to the one extracted from standardly employed four-point correlation functions. Our numerical results are in qualitative agreement with IMCT predictions but suggest that one has to take into account fluctuations not included in this mean-field approach to reach quantitative agreement. Advantages of our approach over the more conventional one based on four-point correlation functions are discussed.