Part 1: Silvio Franz and Giorgio Parisi The simplest model of jamming

Since 2009, Journal of Physics A has awarded a Best Paper Prize, which serves to celebrate well written papers that make a significant contribution to their field. In 2017, the Editorial Board have awarded three prizes using the criteria of novelty, achievement, potential impact and presentation.

In the first of a series of three interviews, meet Silvio Franz and Giorgi Parisi, the authors of The simplest model of jamming Silvio Franz and Giorgio Parisi 2016 *J. Phys. A: Math. Theor*. **49** 145001.

### Meet the authors

Silvio Franz is Professor at Université Paris-Sud and works at the Laboratory of Theoretical Physics and Statistical Models. Giorgio Parisi is Professor at the University of Rome ‘La Sapienza‘.

### What prompted you to pursue this field of research?

The problem of packing and jamming of hard sphere systems, which have attracted a lot of attention in the context of glass physics in the last years, appears to be a particular Constraint Satisfaction Problem (CSP), where one is searching for values of a set of variables that obey to a set of constraints. Statistical Physics has led to spectacular advances in understanding these problems in the typical case -i.e. when constraints are random-, and when the variables are discrete. In the case of spheres the variables are continuous, it was natural for us to search for the simplest abstract CSP with continuous variables and compare its physics with the one of sphere packing.

### What is the winning paper all about?

The paper studies the Perceptron and related models. There are two regimes: one where the associated CSP is convex and the other where it is non-convex. It turns out that jamming is non-critical in the convex regime, while criticality is associated to non-convexity. The criticality is crucially associated to the fact that the jamming line lies in a glassy phase, rather than in a liquid one. Moreover, it turns out that the model has the same critical exponents as infinite dimensional spheres. This led naturally to the conjecture that there is a unique universality class for jamming in continuous CSP.

### What do you plan to do next?

The “negative Perceptron” emerges as a minimal exactly solvable glass and jamming model. We have already shown that it provides a study of low energy glassy excitations. We are currently studying the low temperature properties in a quantum version of the model, which could provide a hint for the anomalous low temperature properties of glasses.

To see the rest of the winners and the nomination process for the Journal of Physics A Best Paper Prize 2018, visit this page.

Giorgio Parisi’s work has been highlighted as part of our 50th Anniversary Viewpoints collection. Read more here: The discovery of the broken symmetry of replicas

This work is licensed under a Creative Commons Attribution 3.0 Unported License. Images used with permission from the authors.

Categories: Journal of Physics A: Mathematical and Theoretical, JPhys+