On the solution of a `solvable’ model of an ideal glass of hard spheres displaying a jamming transition

Marc Mezard ¹, Giorgio Parisi ², Marco Tarzia ³, Francesco Zamponi ⁴

Journal of statistical mechanics-theory and experiment (2011) P03002

We discuss the analytical solution through the cavity method of a mean field model that displays at the same time an ideal glass transition and a set of jamming points. We establish the equations describing this system, and we discuss some approximate analytical solutions and a numerical strategy to solve them exactly. We compare these methods and we get insight into the reliability of the theory for the description of finite dimensional hard spheres.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud
• 2. Dipartimento di Fisica,
  Università Roma I
• 3. Laboratoire de Physique Théorique de la Matière Condensée (LPTMC),
  CNRS : UMR7600 – Université Paris VI – Pierre et Marie Curie
• 4. Laboratoire de Physique Théorique de l’ENS (LPTENS),
  CNRS : UMR8549 – Université Paris VI – Pierre et Marie Curie – Ecole Normale Supérieure de Paris – ENS Paris