Glassy behaviour in short range lattice models without quenched disorder

We investigate the quenching process in lattice systems with short range interaction and several crystalline states as ground states. We consider in particular the following systems on square lattice:

• hard particle (exclusion) model;
• q states planar Potts model. The system is initially in a homogeneous disordered phase and relaxes toward a new equilibrium state as soon as the temperature is rapidly lowered. The time evolution can be described numerically by a stochastic process such as the Metropolis algorithm. The number of pure, equivalent, ground states is q for the Potts model and r for the hard particle model, and it is known that for r or q larger or equal to d+1, the final equilibrium state may be polycrystalline, i.e. not made of a uniform phase. We find that in addition n_g and q_g exist such that for r > r_g, or q > q_g the system evolves toward a glassy state, i.e. a state in which the ratio of the interaction energy among the different crystalline phases to the total energy of the system never vanishes; moreover we find indications that r_g=q_g. We infer that q=q_g (and r=r_g) corresponds to the crossing from second order to discontinuous transition in the phase diagram of the system.