Statics and dynamics of infinite-dimensional liquids and glasses: a parallel, compact derivation

Understand

We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases.

• The static derivation is based on the introduction of an "auxiliary" disorder and the use of the replica method.
• The dynamic derivation is based on the general analogy between replicas and the supersymmetric formulation of dynamics.
• We show that static and dynamic results are consistent, and follow the Random First Order Transition scenario of mean field disordered glassy systems.