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Search for an experimental test of the mean-field theory of simple glasses

Periodic Reporting for period 1 - EXPMFSG (Search for an experimental test of the mean-field theory of simple glasses)

Reporting period: 2015-07-16 to 2017-07-15

The goal of my project was to provide a precise test for the recent mean field theory for simple glasses, first numerical, and at a second stage, experimental. Among the predictions of the theory, the most unexpected and relevant for the field was the prediction of a new phase transition inside the glass phase, separating two kinds of glasses: a standard glass, akin to a crystal, and a marginal one, akin to a spin glass, where vibrations would be strongly correlated both in time and space. This transition is known as the Gardner transition due to the analogy to the transition predicted by Gardner in certain models of spin glasses more than 30 years ago. While the existence of this transition in magnetic system was nothing more than a curiosity, it has attracted great attention in the field of glasses. The reason is simple, the mere existence of the new glass phase would provide a first-principles and universal explanation for the anomalies of amorphous solids with respect to the Debye theory of solids (i.e. the abundance of low energy modes, the ‘boson peak’, anomalous scalings with of the heat capacity or conductivity with the temperature, drastic and irreversible response to tiny perturbations, etc.), thus paving the way for the development of a theory for amorphous solids.

This project has focused the attention in determining the existence of the Gardner transition in realistic systems, both in simulations and experiments. This task represented a great challenge three years ago, mainly because such a transition had never been observed, even though decades of intense investigation of these materials (even in the relevant parameter space).
Since it was clear that traditional approaches did not see the Gardner transition, our main initial task was to explore several protocols and observables in a well controlled model where the Gardner transition existed for sure. With this idea, we studied in simulations a mean-field model for hard-spheres that allows an analytical description at any dimension. Using this model, and trying old spin glasses ideas, we where able to design a successful numerical protocol based on two observables: the traditional mean-square displacement, and the distance between two clones, where clones corresponded to independent compressions of the system which all started from the same configuration [1]. After testing the approach in the mean-field model, we moved to real hard spheres. We repeated the same protocol in D=2 and 3 in Ref. [2]. We were able to show, by the first time, the existence of a sharp threshold in density above which vibrations become highly correlated. Furthermore, we could also associate this threshold to a divergence of time and length-scales, as expected nearby a second order transition and a non-trivial change of the probability distribution function of the order parameter. Quite remarkably, the protocol proposed in our works [1] and [2] was suitable to be directly repeated in experiments of frictional hard disks [3], thus providing the first experimental test of the Gardner transition.

After testing the theory in hard-sphere systems, the canonical model for granulars or colloids, we explored the existence of a Gardner transition
in temperature in a simple model for molecular glasses in prepared via the vapor deposition procedure. We concluded that, although a Gardner-like threshold is observed at low temperatures, and that this threshold depends on the stability of the original glass, the transition changes its nature when thermal fluctuations are introduced. The threshold is not longer sharp, and it is not related to the apparition of collective excitations but localized ones. In this sense, we find a threshold in temperature but it does not lead to a marginal phase but it is related to localized defects in the sample [4]. Still, many of the anomalies remain visible.

The protocol followed in Refs. [1,2,4] can only be repeated in experiments if spatial resolution is available (like in granular disks), which is not generally the case in most of glassy systems. For this reason, I have also worked in developing new alternative protocols based only on macroscopic observables. During the project, I tested these ideas first in spin glasses [5,6] and I have recently applied to hard-sphere problems, but this work is still ongoing.

[1] Charbonneau, P., Jin, Y., Parisi, G., Rainone, C., Seoane, B., & Zamponi, F. (2015). Numerical detection of the Gardner transition in a mean-field glass former. Physical Review E, 92(1), 012316.
[2] Berthier, L., Charbonneau, P., Jin, Y., Parisi, G., Seoane, B., & Zamponi, F. (2016). Growing timescales and lengthscales characterizing vibrations of amorphous solids. Proceedings of the National Academy of Sciences, 201607730.
[3] Seguin, A., & Dauchot, O. (2016). Experimental Evidence of the Gardner Phase in a Granular Glass. Physical review letters, 117(22), 228001.
[4] Seoane, B., Reid, D. R., de Pablo, J. J., & Zamponi, F. (2017). Low-temperature anomalies of a vapor deposited glass. arXiv preprint arXiv:1709.04930.
[5] Baity-Jesi, M., Calore, E., Cruz, A., Fernandez, L. A., Gil-Narvión, J. M., Gordillo-Guerrero, A., ... & Monforte-Garcia, J. (2017). A statics-dynamics equivalence through the fluctuation–dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements. Proceedings of the National Academy of Sciences, 201621242.
[6] Baity-Jesi, M., Calore, E., Cruz, A., Fernandez, L. A., Gil-Narvion, J. M., Gordillo-Guerrero, A., ... & Monforte-Garcia, J. (2017). Matching microscopic and macroscopic responses in glasses. Physical Review Letters, 118(15), 157202.
Besides the theoretical significance of the Gardner transition, its existence and consequences will have a great relevance in materials science. First, because it provides a first-principles explanation for the universal anomalies in amorphous solids, which paves the way to the development of a theory for amorphous solids. Second, because it provides a conceptual framework to construct better glasses (for industry), which would be those where the Gardner transition occurred at very low temperatures or were nonexistent. Indeed, the stable glass phase is more stable against perturbations, which makes it more elastic and resistant to fracture, for instance.