Disordered backgammon model

In this paper we consider an exactly solvable model that displays glassy behavior at zero temperature due to entropic barriers. The new ingredient of the model is the existence of different energy scales or modes associated with different relaxational time scales. Low-temperature relaxation takes place by partial equilibration of successive lower-energy modes. An adiabatic scaling solution, defined in terms of a threshold energy scale epsilon*, is proposed. For such a solution, modes with energy epsilon>>epsilon* are equilibrated at the bath temperature, modes with epsilon<<epsilon* remain out, of equilibrium, and relaxation occurs in the neighborhood of the threshold epsilon similar toe*. The model is presented as a toy example to investigate the conditions related to the existence of an effective temperature in glassy systems and its possible dependence on the energy sector is probed by the corresponding observable.