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## Recent advances on the glass problem

#### on-line, hosted by CECAM-HQ

#### Organisers

**PLEASE NOTE THAT THE IN-PERSON WORKSHOP HAS BEEN CANCELLED AND MOVED ONLINE,
as last-year edition (https://www.cecam.org/workshop-details/1019).**

This workshop will consists of three online sessions:

**Day 1 [chair: E. Agoritsas]**

*Speakers*: P. Harrowell, M. Baity Jesi, I. Procaccia, P. Urbani.

**Day 2 [chair: P. Charbonneau]**

*Speakers*: T. Voigtmann, J. C. Dyre, A. Altieri, S. Patinet, A. Liu, F. Ricci-Tersenghi.

**Day 3 [chair: L. Berthier]**

*Speakers*: M. Leocmach, M. Paoluzzi, S. Henkes, C. O'Hern, E. Corwin.

Each day includes a two-hour-and-a-half block on Zoom of presentations and group discussions. Note that there will be no poster session. In order to receive the Zoom links, you will need to register to the workshop via the specific tab 'Participate' (you will need a CECAM account first).

*Description*

Glass – the prototypic and ubiquitous amorphous solid – inhabits a complex and ramified energy landscape. Dealing with the plethora of relevant energy minima has emerged as one of the central problems of statistical physics. The mere existence of a glass reveals organizational principles that are dramatically different from those of ordered solids and poses the fundamental question: is there a limit of absolute disorder that is the opposite pole from the perfect order of a crystal? For crystals, the minimization of a function of 10^23 variables (e.g., a system’s free energy with respect to its degrees of freedom) is reduced to finding a few competing minima; for glasses, the gigantic degeneracy of low-energy minima leads to a spectacular failure of conventional approaches.

Because a supercooled liquid that solidifies into a glass results from the system’s failure to fully explore its energy landscape, statics and dynamics are inextricably linked. The transition into a glass is therefore an entirely different phenomenon from the transition into a crystal [1-2]. Just as the physics of the glass state defies concepts from ordinary solid-state physics, the glass transition defies ordinary phase-transition theory.

Cooling a liquid to low temperatures (the glass transition) and compressing a zero-temperature disordered collection of particles (the jamming transition) are two ways of obtaining amorphous solids [3-6]. Jamming is athermal and static, and is in some ways simpler than glass formation, where thermal and dynamical effects also play crucial roles [7-8], yet also presents a remarkably rich phenomenology.

Recent advances in the glass field have discovered and characterized the jamming transition for dimension d≥2 and obtained a solution for the statics and the dynamics of liquids in the mean-field, d->∞ limit [9-11]. These theoretical advances provide a unifying framework that includes a third transition, the Gardner transition, that separates jamming from glass formation [12]. The recent development of a field-theoretic framework to describe glassy dynamics and associated length scales for systems with many energy minima away from d=∞ [13-14] as well as a harmonic theory for jammed solids near zero temperature [15] further provide two broad insights, which make this workshop particularly timely: (i) the crucial role played by dimension as a control parameter for analyzing the statics and the dynamics of glassy matter, and (ii) the realization that real-space and phase-space approaches converge to the same critical exponents.

A number of these advances would have been impossible without the constant support, confrontation and validation from computational sciences. This research program has indeed benefited from and stimulated a vast program of molecular simulations, in order to both test the theoretical ideas and to provide a bridge between the mean-field results and physical systems in d=2,3 [16-18]. New computational concepts and algorithms are pushing forward our numerical capabilities far beyond what was once considered conceivable, and are currently playing a central role in solving the glass problem [19-20].

## References

**France**

Ludovic Berthier (CNRS) - Organiser

Francesco Zamponi (ENS Paris) - Organiser

**Switzerland**

Elisabeth Agoritsas (University of Geneva) - Organiser

**United States**

Patrick Charbonneau (Duke University) - Organiser