2018 Simons Collaboration on Cracking the Glass Problem Annual Meeting

The second annual meeting of the Cracking the Glass Problem Collaboration took place on March 8-9, 2018, at the Simons Foundation in New York. It gathered together a group of 69 researchers from the USA, Europe, Japan and India. It featured stimulating talks by collaboration scientists and distinguished external speakers, as well as a poster session by the other members of the collaboration. The excellent setting provided by the Simons Foundation enabled a very interactive environment that fostered vibrant discussions among the diverse crowd of attending scientists.

The collaboration’s goal is to develop a complete and quantitative description of the glass transition, connecting the explicit and quantitative mean-field and zero-temperature theories that have been pioneered by the collaborators. The aim is to develop a similarly quantitative and predictive theory of glassy dynamics in finite dimensions at finite temperatures. The tools developed in creating this framework will have important ramifications in a wide range of fields outside of physics, including computer science (e.g., in optimization problems) and the development of machine-learning techniques. Over the last one and a half years, the collaboration has made major breakthroughs: it obtained a full characterization of a new phase of amorphous solids, it paved the way toward a full theory of how glasses yield and lose their rigidity, and it introduced new, very powerful algorithms that enable simulations of supercooled liquids in regimes completely out of reach until now.

One of the major results that has enabled the Cracking the Glass Problem Collaboration has been the discovery in the mean-field limit of the Gardner transition — a proposed transition where the energy landscape that characterizes the glass becomes fractal, with states (configurations) organized in a hierarchical manner inside ever larger groupings of states. Starting in 2014, Cracking the Glass Problem collaborators demonstrated that the Gardner transition is an essential feature of the mean-field (i.e., infinite-dimensional) solution of the hard-sphere glass transition. At the meeting, Ludovic Berthier summarized the collaboration’s progress in understanding the Gardner transition. Importantly, he noted that, due to the efforts of many collaboration members over the last one and half years, the basic outlines of a complete solution to the Gardner transition is now at hand. This complete understanding comes from a synergistic combination of theory (including new, non-perturbative Renormalization-Group results) as well as simulations in a variety of in silico systems. These results illustrate that the Gardner transition is highly relevant for the jamming transition, and potentially relevant for thermal systems with near hard-sphere-like interactions. Future work will be devoted to a more detailed understanding of the systems and conditions for which the Gardner transition predicts experimentally observable consequences, the relationship between the Gardner transition and the putative two-level tunneling systems in glasses at ultra-low temperatures and related questions.

On the computational side, Patrick Charbonneau discussed the myriad studies and scientific questions enabled by the large-scale computer simulations that employ the new revolutionary swap Monte Carlo algorithm developed by collaboration members. This new approach allows for the thermalization of glassy systems over a range that is, in some systems, even wider than that provided in experimental systems studied in the laboratory. A major question arising from the efficacy of the swap algorithm was pointed out this year by collaboration member Matthieu Wyart and Michael Cates: Does the success of swap Monte Carlo imply that collective thermodynamic correlations are irrelevant for the slowing of dynamics as the glass transition is approached from higher temperature? Charbonneau outlined various scenarios that could be consistent with the ability of swap Monte Carlo to equilibrate glassy samples rapidly. A large set of complementary efforts sparked by this question has nucleated, and we expect spirited discussion of this issue to continue into the next year of the collaboration.

Matthieu Wyart summarized the collaboration’s progress in the realm of glassy rheology. He discussed how the swap Monte Carlo algorithm mentioned above has enabled the study of previously unreachable phenomena, such as brittle yielding in glasses. He summarized the success of the collaboration in developing a mean-field theory of yielding and outlined the ongoing efforts to merge this mean-field theory with a real-space approach to address questions such as crackling, shear-banding and the ductile-to-brittle-phase transition. Lastly, he summarized open issues related to the physics of driven liquids and the emergence and role of two-level systems in glassy rheology.

David Reichman gave a perspective on what has been accomplished and where the collaboration is heading in the description of the dynamics of glassy systems. He first discussed the real-space description of avalanche processes and gave an overview of the open questions related to the behavior of dynamical heterogeneities as a system approaches the glass transition. This important issue can now be probed because of the computational breakthroughs of the collaboration both in terms of in silico sample preparation (via swap Monte Carlo) and algorithms based on machine learning to detect soft regions in amorphous systems. He then discussed dynamics from an energy landscape perspective, explicating the importance of computationally finding transition pathways on the rough energy landscape that connect to the real-space collective motion of particles. He suggested path-finding methods such as those pioneered by Eric Vanden Eijnden (discussed by him in a subsequent lecture) to accomplish this goal. Lastly, he recapitulated the important breakthrough of collaboration members in solving the exact dynamics of hard-sphere liquids in infinite dimensions. He speculated on effective ways to incorporate finite-dimension corrections into this solution.

In addition to Vanden Eijnden, other guests gave highly stimulating and pertinent lectures at the meeting. Karen Daniels (from the experimental perspective) and Daan Frenkel (from a computational perspective) gave talks related to the open issue of how to count and weigh configurations of athermal jammed packings of particles.

After the first two days of the workshop, smaller breakout discussions on dynamics, as well as a weekend meeting of postdocs and students, took place at Columbia University. The successful synergy of the collaboration was aptly summarized by Daan Frenkel at the start of his talk when he observed that he had never seen a large, funded collaborative effort work effectively until he witnessed the efforts of the Cracking the Glass Problem team at our annual meeting. Overall, the meeting highlighted the great progress made over the last year, as well as important new directions that will pave the way for future discoveries.

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