  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.

Statistical Mechanics