Matrix Models as Solvable Glass Models

We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter p. For p = 2 we obtain matrix models and for p ? 2 `tensor' models. We concentrate on the cases p = 2 which we study analytically and numerically. 75.10.Nr, 64.60.Cn, 64.70.Pf, 11.17.+y Typeset using REVT E X Address after October 1st: Service de Physique de l'Etat Condens'e, CEA, Saclay, France. y Address after October 1st: LPTHE, Ecole Normale Sup'erieure, Paris, France. Disordered systems such as structurally disordered materials (glasses) and spin-glasses are characterized by complex free-energy landscapes and non-equilibrium phenomena with time-scales exceeding the experimental times [1--5]. The glass transition being mainly kinetic, one has to face the full dynamical problem in order to grasp many aspects of the physical behavior of these systems. Thi..