Browsing by Author "Yaida, Sho"

Now showing 1 - 7 of 7

Open Access
Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling.
(Proceedings of the National Academy of Sciences of the United States of America, 2017-10-10) Berthier, Ludovic; Charbonneau, Patrick; Coslovich, Daniele; Ninarello, Andrea; Ozawa, Misaki; Yaida, Sho
Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, because of the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally relevant timescales. In this work, we not only close the colossal gap between experiments and simulations but manage to create in silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.
Open Access
Efficient measurement of point-to-set correlations and overlap fluctuations in glass-forming liquids.
(J Chem Phys, 2016-01-14) Berthier, Ludovic; Charbonneau, Patrick; Yaida, Sho
Cavity point-to-set correlations are real-space tools to detect the roughening of the free-energy landscape that accompanies the dynamical slowdown of glass-forming liquids. Measuring these correlations in model glass formers remains, however, a major computational challenge. Here, we develop a general parallel-tempering method that provides orders-of-magnitude improvement for sampling and equilibrating configurations within cavities. We apply this improved scheme to the canonical Kob-Andersen binary Lennard-Jones model for temperatures down to the mode-coupling theory crossover. Most significant improvements are noted for small cavities, which have thus far been the most difficult to study. This methodological advance also enables us to study a broader range of physical observables associated with thermodynamic fluctuations. We measure the probability distribution of overlap fluctuations in cavities, which displays a non-trivial temperature evolution. The corresponding overlap susceptibility is found to provide a robust quantitative estimate of the point-to-set length scale requiring no fitting. By resolving spatial fluctuations of the overlap in the cavity, we also obtain quantitative information about the geometry of overlap fluctuations. We can thus examine in detail how the penetration length as well as its fluctuations evolve with temperature and cavity size.
Open Access
Lyapunov exponent and susceptibility
(2017-08-23) Charbonneau, Patrick; Li, Yue Cathy; Pfister, Henry D; Yaida, Sho
Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with imperfect measurement of the initial conditions. Finite-time estimates of the exponent, however, experience fluctuations due to both the initial condition and the stochastic nature of the dynamical path. The scale of these fluctuations is governed by the Lyapunov susceptibility, the finiteness of which typically provides a sufficient condition for the law of large numbers to apply. Here, we obtain a formally exact expression for this susceptibility in terms of the Ruelle dynamical zeta function. We further show that, for systems governed by sequences of random matrices, the cycle expansion of the zeta function enables systematic computations of the Lyapunov susceptibility and of its higher-moment generalizations. The method is here applied to a class of dynamical models that maps to static disordered spin chains with interactions stretching over a varying distance, and is tested against Monte Carlo simulations.
Open Access
Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class
Charbonneau, Patrick; Hu, Yi; Raju, Archishman; Sethna, James P; Yaida, Sho
A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point but, given the uncontrolled nature of perturbative analysis in the strong-coupling regime, debate persists. Here we examine the nature of the transition as a function of spatial dimension and show that the strong-coupling fixed point can go through a Hopf bifurcation, resulting in a critical limit cycle and a concomitant discrete scale invariance. We further investigate a different renormalization scheme and argue that the basin of attraction of the strong-coupling fixed point/limit cycle may thus stay finite for all dimensions.
Open Access
Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions.
(Phys Rev Lett, 2017-05-26) Charbonneau, Patrick; Yaida, Sho
The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon-the Gardner transition-has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_{u}=6. Here, we obtain evidence for the existence of these transitions in d
Open Access
Point-to-set lengths, local structure, and glassiness.
(Phys Rev E, 2016-09) Yaida, Sho; Berthier, Ludovic; Charbonneau, Patrick; Tarjus, Gilles
The growing sluggishness of glass-forming liquids is thought to be accompanied by growing structural order. The nature of such order, however, remains hotly debated. A decade ago, point-to-set (PTS) correlation lengths were proposed as measures of amorphous order in glass formers, but recent results raise doubts as to their generality. Here, we extend the definition of PTS correlations to agnostically capture any type of growing order in liquids, be it local or amorphous. This advance enables the formulation of a clear distinction between slowing down due to conventional critical ordering and that due to glassiness, and provides a unified framework to assess the relative importance of specific local order and generic amorphous order in glass formation.
Open Access
Zero-temperature glass transition in two dimensions
Berthier, Ludovic; Charbonneau, Patrick; Ninarello, Andrea; Ozawa, Misaki; Yaida, Sho
The nature of the glass transition is theoretically understood in the mean-field limit of infinite spatial dimensions, but the problem remains totally open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to control analytically, and experiments fail to provide conclusive evidence regarding the nature of the glass transition. Here, we use Monte Carlo simulations that fully bypass the glassy slowdown, and access equilibrium states in two-dimensional glass-forming liquids at low enough temperatures to directly probe the transition. We find that the liquid state terminates at a thermodynamic glass transition at zero temperature, which is associated with an entropy crisis and a diverging static correlation length.