The first annual meeting of the Cracking the Glass Problem collaboration took place March 9–10, 2017 at the Simons Foundation in New York. It gathered together a group of 65 researchers from USA, Europe, Japan, India and Brazil. It featured exciting talks by collaboration scientists and by distinguished external speakers, and a poster session by the other members of the collaboration. The great 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 dimension at finite temperatures. The tools developed in creating such a framework will have important ramifications in a wide range of fields.
The progress made by the collaboration in the first year, which was summarized by director Sidney Nagel, includes crucial new theoretical results and the development of powerful new algorithms that will greatly increase our understanding of amorphous matter and enable the in silico study of glassy systems in regimes heretofore impossible. In addition, there was substantial progress on another stated goal of the collaboration: connecting glass physics with other areas of science such as biology and computer science.
One of the major breakthroughs that has enabled the Cracking the Glass 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 (infinite-dimensional) solution of the hard sphere glass transition. In this meeting, Patrick Charbonneau gave a talk that summarized the features and successes of this work. In particular, the theory can make a precise prediction of non-trivial scaling exponents for the jamming transition. This is the zero-temperature transition to a marginally stable disordered glass. Surprisingly the exponents appear to apply even in the two- and three- dimensional cases of relevance to experiments. Charbonneau went on to show results of new computer simulations in systems, including crystalline systems, which strikingly illustrate phenomenology consistent with a Gardner phase.
Sho Yaida gave a talk on recent research that likely provides a resolution to two enduring puzzles in the community: (i) Why are their strong signs of the existence of a Gardner transition in simulations and experiments when all previous calculations found that the upper critical dimension for the transition is 6? (ii) If there indeed is a transition in two and three dimensions, why do the exponents conform to their mean-field values calculated in detail in the past by collaboration members? Yaida showed results from 2- and 3-loop (Padé re-summed) renormalization group calculations showing the existence of a strong-coupling Gardner fixed point as shown in the figure above. This suggests that both the upper and lower critical dimensions of the Gardener transition may in fact be two.
On the computational side, Ludovic Berthier showed results from large-scale computer simulations that employ a new Monte Carlo algorithm (“swap” Monte Carlo) which allows for thermalization of glassy systems over a range that is, in some cases, wider than that provided in experimental systems studied in the laboratory. This is shown in the figure at the right. This is a ground-breaking result, as was pointed out by James Sethna who serves as scientific advisor to the collaboration. With this approach, Berthier provided compelling evidence that a “holy-grail” question in the glass-transition field, namely the existence of the putative Kauzmann or ideal glass transition (an underlying singularity at finite temperature governing the laboratory glass transition) may be answered in the affirmative. This was the strongest evidence yet in favor of such a singularity.
Lastly, many interesting results were presented for problems at the intersection of the glass problem and other fields. For example, Lisa Manning presented exciting results showing the connections between jamming and rigidity and flow in biological tissues, while Gerard Ben Arous and Andrea Montanari discussed aspects of machine learning problems which are connected to the glass transition problem. 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.
Elisabeth Agoritsas ENS Paris Yevgeny Bar Lev Columbia University Gerard Ben Arous NYU Ludovic Berthier Montpellier University Patrick Charbonneau Duke University Eric De Giuli EPFL Lisa Manning Syracuse University Andrea Montanari Stanford Sidney Nagel University of Chicago Jim Sethna Cornell University Gilles Tarjus UPMC Sho Yaida Duke University