  We consider the dynamics of a disordered p-spin model with p=2, analyzing the
dynamics within Ruelle's thermodynamic formalism, We use an indicator of the
dynamical activity to construct the relevant dynamical Gibbs ensemble. We prove
that the dynamics in the low-temperature (spin glass) phase of the model take
place at a second-order phase transition between dynamically active and
inactive trajectories. We also show that the same behaviour is found in a
related model of a three-dimensional ferromagnet.
