A new critical phase in jammed models: jamming is even cooler than before
Online defense – Zoom Meeting ID: 940 6511 8835 – Password: 520321
Jean-Louis Barrat, Université Grenoble-Alpes, examinateur
Giuseppe Foffi, Université Paris-Saclay, examinateur
Silvio Franz, LPTMS, directeur de thèse
Luca Leuzzi, Consiglio Nazionale delle Ricerch, rapporteur
Andrea Liu, University of Pennsylvania, examinatrice
Markus Müller, Paul Scherrer Institut, rapporteur
Pierfrancesco Urbani, CNRS, CEA Saclay, examinateur
Matthieu Wyart, École Polytechnique Fédérale de Lausanne, examinateur
Over the last two decades, an intensive stream of research has characterized the jamming transition, a zero-temperature critical point of systems with short-range repulsive interactions. Many of its properties are independent of spatial dimensionality, with mean-field scalings being valid even for two-dimensional systems.
In this thesis, we extend this critical behavior from the jamming transition point to an entire jammed phase. This is obtained by using a short-range linear repulsive interaction potential for soft spheres and for a related mean-field model, i.e. the perceptron.We show that the non-differentiable point in the pairwise interaction potential produces a network of tangent spheres (a “contact network”) at every density beyond the jamming transition. The contact networks characterizing the minima of the system are isostatic, critically self-organized and marginally stable.
In the first part, we study the jammed phase of the perceptron, both numerically and theoretically using techniques developed for mean-field glassy systems. We show the presence of a critical phase and we develop a zero-temperature scaling theory which establishes its universality class.Therefore, we use numerical simulations to study the soft spheres case in two and three dimensions and we point out the presence of the critical jammed phase also in finite dimensions.
In the second part, we define a compression protocol for the perceptron that allows us to study the avalanche dynamics in the critical phase. We show that the avalanche sizes are scale-free power law distributed with divergent first moment and we characterize the finite-size scalings. Our numerical results are robustly consistent with the mean-field theory.
This work shows the existence of a new critical phase in finite dimensions whose universality is strongly connected to the class of jamming universality. This opens new perspectives to study marginally stable glasses and their related energy landscapes.