(IPhT, CEA, Saclay.)
Critical exponents of the jamming transition
Jammed packings of hard spheres are well known marginally stable systems. They are isostatic and display power laws in the distributions of contact forces and of spheres in quasi-contact. I will discuss the solution of the hard sphere model in the limit of infinte dimensions from which we can derive analytically both the power laws and the values of the corresponding exponents. Close to jamming a new transition, the Gardner transition, is found. The high pressure phase is characterized by a new free energy landscape whose features are deeply related with the marginal stability properties of jammed packings. Remarkably, this new free energy landscape is very close to what is found in the solution of the Sherrington-Kirkpatrick spin glass model. The values of the exponents are compatible with both a recently proposed scaling theory of the jamming transition and numerical simulations in finite dimensions. Finally, I will discuss a perturbative renormalization group analysis of the Gardner transition in finite dimensions.