Mean-field avalanches in jammed spheres.
By Silvio Franz, Stefano Spigler. 2016
44 citations recorded by the source corpus.
Disordered systems are characterized by the existence of many sample-dependent local-energy minima that cause a step-wise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three-dimensional systems of soft spheres, either at jamming or at slightly higher densities.
Subfields: Condensed Matter Physics, Global and Planetary Change, Materials Chemistry, AI for Physical Sciences
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Condensed Matter Physics
- Pierfrancesco Urbani
- Francesco Zamponi
- Silvio Franz
- Giorgio Parisi
- Matthieu Wyart
- Stefano Spigler
- Giulio Biroli
- Maksim Sevelev
In Global and Planetary Change
In Materials Chemistry
- Pierfrancesco Urbani
- Giorgio Parisi
- Francesco Zamponi
- Silvio Franz
- Stefano Spigler
- Matthieu Wyart
- Giulio Biroli
- Mario Geiger
In AI for Physical Sciences
- Pierfrancesco Urbani
- Francesco Zamponi
- Giorgio Parisi
- Silvio Franz
- Matthieu Wyart
- Stefano Spigler
- Mario Geiger
- Stéphane d'Ascoli
Citations in the corpus
- The jamming transition as a paradigm to understand the loss landscape of deep neural networks (2018, background): “The inequality comes from arguments on the stability of jammed packings, and the fact that it is saturated (which can be proven for certain dynamics [43]) implies that such systems are marginally stable: they display an abundance of low-energy excitations and are prone to avalanche dynamics and crac”
- Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems (2017, background): “Also, it has been shown in [19] that the asymptotic behavior of the function y(q), related to the exponent κ, controls the scaling of the avalanches at the jamming point, which is therefore different than the scaling in the UNSAT phase.”