Fast Relaxation Time in a Spin Model with Glassy Behavior

We consider a frustrated spin model with a glassy dynamics characterized by a slow component and a fast component in the relaxation process. The slow process involves variables with critical behavior at finite temperature Tp and has a global character like the (structural) α-relaxation of glasses. The fast process has a more local character and can be associated to the β-relaxation of glasses. At temperature T > Tp the fast relaxation follows the non-Arrhenius behavior of the slow variables. At T . Tp the fast variables have an Arrhenius behavior, resembling the α − β bifurcation of fragile glasses. The model allows us to analyze the relation between the dynamics and the thermodynamics.