Abstract
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 a square lattice: hard-core particles with r ground states; and the q-state planar Potts model. The system is initially in a homogeneous disordered phase and relaxes towards a new equilibrium state as soon as the temperature is rapidly lowered. Its evolution can be described numerically by a stochastic process such as the Metropolis algorithm and it is known that for r or q ⩾ d + 1 the final equilibrium state may be polycrystalline, that is not made of a uniform phase. We find that, in addition, r g and q g exist such that for r > r g or q > q g the system evolves towards a glassy state, that is a state in which the ratio of the interaction energy between 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, for the Potts model, q = q g corresponds to the crossing from second order to discontinuous transition in the phase diagram of the system.