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A localization transition underlies the mode-coupling crossover of glasses

by Daniele Coslovich, Andrea Ninarello, Ludovic Berthier

Submission summary

As Contributors: Daniele Coslovich · Andrea Ninarello
Arxiv Link: (pdf)
Date accepted: 2019-11-15
Date submitted: 2019-10-08 02:00
Submitted by: Coslovich, Daniele
Submitted to: SciPost Physics
Academic field: Physics
  • Statistical and Soft Matter Physics
Approach: Computational


We study the equilibrium statistical properties of the potential energy landscape of several glass models in a temperature regime so far inaccessible to computer simulations. We show that unstable modes of the stationary points undergo a localization transition in real space close to the mode-coupling crossover temperature determined from the dynamics. The concentration of localized unstable modes found at low temperature is a non-universal, finite dimensional feature not captured by mean-field glass theory. Our analysis reconciles, and considerably expands, previous conflicting numerical results and provides a characteristic temperature for glassy dynamics that unambiguously locates the mode-coupling crossover.

Ontology / Topics

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Glasses Mean-field theory (MFT)

Published as SciPost Phys. 7, 077 (2019)

Author comments upon resubmission

We thank the referees for their competent and constructive reports. We have addressed their criticisms and concerns as follows:

  • We have finally performed additional, extensive searches for 'true' stationary points using a different optimization method (eigenvector-following). The new data are presented and discussed in the revised version and allow us to investigate closely the similarities and differences between stationary and quasi-stationary points, as requested by both referees.

  • Prompted by referee 2, we have performed additional analysis of the energy-dependence of stationary points (as opposed to their temperature-dependence). We found that the bare energy reaches the threshold energy at a temperature close to the MCT crossover, in agreement with our analysis in terms of temperature. This new analysis is presented in the new Fig. 2 and corroborates the mapping between instantaneous configurations and stationary points provided by force minimizations, thereby addressing the main concern of referee 2.

  • We have substantially expanded and improved the discussion in the text, to make the presentation more accessible and to clarify all the unclear points indicated by the referees.

  • We also carefully checked again the numerics of all our optimizations, enforcing strict convergence criteria for all studied models.

See our replies to the referees' reports for full details.

With these extensive set of changes, we feel that the quality of the manuscript has substantially improved and that the main physical message of our work (the localization of unstable modes around the MCT crossover) has passed a fairly stringest test. We hope therefore that it will be considered suitable for publication in SciPost.

List of changes

- Add eigenvector-following optimizations for the ternary mixture model. The figures and accompanying discussions have been updated to reflect this new set of data.
- Add analysis of the bare energy as a function of temperature, as suggested by referee 2.
- New Fig. 2, which gathers the analysis on the energy-dependence of the fractions of modes.
- Extend and revise the presentation of the unstable spectrum g(lambda), see new Fig. 6.
- Add panel to the new Fig. 11 in the Appendix, showing f_u(T) for stationary points in all studied models.
- Add plots of the unstable spectrum of all studied models in the Supplementary information.
- Add plots of N-dependence of f_u(e_s) of all studied models in the Supplementary information.
- Several minor fixes and improvements to the text to take into account the remarks of the referees.

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