Equilibrium and dynamics of a multi-bath Sherrington–Kirkpatrick model

Abstract

In this paper we study the equilibrium statistical mechanical as well as the dynamical properties of a Sherrington–Kirkpatrick model in a multi-bath setting introduced in Cugliandolo and Kurchan (1999 Physica A 263 242–51). We show that the free energy per particle in the thermodynamical limit obeys a variational principle of Parisi type. The relation between the resulting order parameters is discussed.