Mean field theory of the swap Monte Carlo algorithm

Transverse forces and glassy liquids in infinite dimensions

We explore the dynamics of a simple liquid whose particles, in addition to standard potential-based interactions, are also subjected to transverse forces preserving the Boltzmann distribution. We derive the effective dynamics of one and two tracer particles in the infinite-dimensional limit. We determine the amount of acceleration of the dynamics caused by the transverse forces, in particular in the vicinity of the glass transition. We analyze the emergence and evolution of odd transport phenomena induced by the transverse forces.

Understanding the swap Monte Carlo algorithm in a size-polydisperse model glassformer

The dynamics of a polydisperse model glassformer are investigated by augmenting molecular dynamics (MD) simulation with swap Monte Carlo (SMC). Three variants of the SMC algorithm are analyzed with regard to convergence and performance. We elucidate the microscopic mechanism responsible for the drastic speed-up of structural relaxation at low temperature. It manifests in a stepwise increase of the mean-squared displacement when the timescale between the application of swap sweeps is significantly larger than a characteristic microscopic timescale. Compared to Newtonian dynamics, with the hybrid MD-SMC dynamics the glass transition shifts to a lower temperature and a different temperature dependence of the localization length is found.

Diffusion-Coefficient Power Laws and Defect-Driven Glassy Dynamics in Swap Acceleration

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 swap model 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 glassy dynamics. At small ϕ_{s}, swap initiators, becoming defect particles, induce remarkably typical glassy dynamics of regular particles. This supports defect models of glass.

Collective dynamics in a glass-former with Mari-Kurchan interactions

We numerically study the equilibrium relaxation dynamics of a two-dimensional Mari-Kurchan glass model. The tree-like structure of particle interactions forbids both non-trivial structural motifs and the emergence of a complex free-energy landscape leading to a thermodynamic glass transition, while the finite-dimensional nature of the model prevents the existence of a mode-coupling singularity. Nevertheless, the equilibrium relaxation dynamics is shown to be in excellent agreement with simulations performed in conventional glass-formers. Averaged time-correlation functions display a phenomenology typical of supercooled liquids, including the emergence of an excess signal in relaxation spectra at intermediate frequencies. We show that this evolution is accompanied by strong signatures of collective and heterogeneous dynamics which cannot be interpreted in terms of single particle hopping and emerge from dynamic facilitation. Our study demonstrates that an off-lattice interacting particle model with extremely simple structural correlations displays quantitatively realistic glassy dynamics.

Transient learning degrees of freedom for introducing function in materials

SignificanceMany protocols used in material design and training have a common theme: they introduce new degrees of freedom, often by relaxing away existing constraints, and then evolve these degrees of freedom based on a rule that leads the material to a desired state at which point these new degrees of freedom are frozen out. By creating a unifying framework for these protocols, we can now understand that some protocols work better than others because the choice of new degrees of freedom matters. For instance, introducing particle sizes as degrees of freedom to the minimization of a jammed particle packing can lead to a highly stable state, whereas particle stiffnesses do not have nearly the same impact.

Mean-field description for the architecture of low-energy excitations in glasses

In amorphous materials, groups of particles can rearrange locally into a new stable configuration. Such elementary excitations are key as they determine the response to external stresses, as well as to thermal and quantum fluctuations. Yet, understanding what controls their geometry remains a challenge. Here we build a scaling description of the geometry and energy of low-energy excitations in terms of the distance to an instability, as predicted, for instance, at the dynamical transition in mean-field approaches of supercooled liquids. We successfully test our predictions in ultrastable computer glasses, with a gapped spectrum and an ungapped (regular) spectrum. Overall, our approach explains why excitations become less extended, with a higher energy and displacement scale upon cooling.

Revisiting the concept of activation in supercooled liquids

In this work, we revisit the description of dynamics based on the concepts of metabasins and activation in mildly supercooled liquids via the analysis of the dynamics of a paradigmatic glass former between its onset temperature [Formula: see text] and mode-coupling temperature [Formula: see text]. First, we provide measures that demonstrate that the onset of glassiness is indeed connected to the landscape, and that metabasin waiting time distributions are so broad that the system can remain stuck in a metabasin for times that exceed [Formula: see text] by orders of magnitude. We then reanalyze the transitions between metabasins, providing several indications that the standard picture of activated dynamics in terms of traps does not hold in this regime. Instead, we propose that here activation is principally driven by entropic instead of energetic barriers. In particular, we illustrate that activation is not controlled by the hopping of high energetic barriers and should more properly be interpreted as the entropic selection of nearly barrierless but rare pathways connecting metabasins on the landscape.

Multiple glass transitions and higher-order replica symmetry breaking of binary mixtures

We extend the replica liquid theory in order to describe the multiple glass transitions of binary mixtures with large size disparities, by taking into account the two-step replica symmetry breaking (2RSB). We determine the glass phase diagram of the mixture of large and small particles in the large-dimension limit where the mean-field theory becomes exact. When the size ratio of particles is beyond a critical value, the theory predicts three distinct glass phases; (i) the one-step replica symmetery breaking (1RSB) double glass where both components vitrify simultaneously, (ii) the 1RSB single glass where only large particles are frozen while small particles remain mobile, and (iii) a glass phase called the 2RSB double glass where both components vitrify simultaneously but with an energy landscape topography distinct from the 1RSB double glass.

Thermal origin of quasilocalized excitations in glasses

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasilocalized modes of the Hessian that grows upon cooling, while others predict a pseudogap D_{L}(ω)∼ω^{α}. To unify these views and observations, we generate glassy configurations of controlled gap magnitude ω_{c} at temperature T=0, using so-called breathing particles, and study how such gapped states respond to thermal fluctuations. We find that (i) the gap always fills up at finite T with D_{L}(ω)≈A_{4}(T)ω^{4} and A_{4}∼exp(-E_{a}/T) at low T, (ii) E_{a} rapidly grows with ω_{c}, in reasonable agreement with a simple scaling prediction E_{a}∼ω_{c}^{4} and (iii) at larger ω_{c} excitations involve fewer particles, as we rationalize, and eventually become stringlike. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudogap distribution is populated with its magnitude rapidly decreasing at lower T. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a stringlike relaxation occurring near the glass transition.

Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions

The recent implementation of a swap Monte Carlo algorithm (SWAP) for polydisperse glass forming mixtures bypasses computational sluggishness and closes the gap between experimental and simulation timescales in physical dimensions d=2 and 3. Here, we consider suitably optimized systems in d=2,3,⋯,8 to obtain insights into the performance and underlying physics of SWAP. We show that the speedup obtained decays rapidly with increasing the dimension. SWAP nonetheless delays systematically the onset of the activated dynamics by an amount that remains seemingly finite in the limit d→∞. This shows that the glassy dynamics in high dimensions d>3 is now computationally accessible using SWAP, thus opening the door for the systematic consideration of finite-dimensional deviations from the mean-field description.

The race to the bottom: approaching the ideal glass?

Key to resolving the scientific challenge of the glass transition is to understand the origin of the massive increase in viscosity of liquids cooled below their melting temperature (avoiding crystallisation). A number of competing and often mutually exclusive theoretical approaches have been advanced to describe this phenomenon. Some posit a bona fide thermodynamic phase to an 'ideal glass', an amorphous state with exceptionally low entropy. Other approaches are built around the concept of the glass transition as a primarily dynamic phenomenon. These fundamentally different interpretations give equally good descriptions of the data available, so it is hard to determine which-if any-is correct. Recently however this situation has begun to change. A consensus has emerged that one powerful means to resolve this longstanding question is to approach the putative thermodynamic transition sufficiently closely, and a number of techniques have emerged to meet this challenge. Here we review the results of some of these new techniques and discuss the implications for the existence-or otherwise-of the thermodynamic transition to an ideal glass.