Glassy Behavior in an Exactly Solvable Spin Model

We introduce a simple spin model which shows glassy behavior at low temperatures, despite a Hamiltonian which is completely homogeneous and possesses no randomness; ergodicity breaking in this model is due entirely to the model's dynamics. We solve exactly for the model's equilibrium partition function, calculate the distribution of energy barriers and equilibrium time scales, and give an expression for the deviation from equilibrium at low temperatures as an expansion in terms of these analytic calculations. We also show that the model does not possess a sharp glass transition, falling out of equilibrium at a temperature which decreases slowly as a function of the cooling rate.