  We numerically study a nondisordered lattice spin system with a first order
liquid-crystal transition, as a model for supercooled liquids and glasses.
Below the melting temperature the system can be kept in the metastable liquid
phase, and it displays a dynamic phenomenology analogous to fragile supercooled
liquids, with stretched exponential relaxation, power law increase of the
relaxation time and high fragility index. At an effective spinodal temperature
Tsp the relaxation time exceeds the crystal nucleation time, and the
supercooled liquid loses stability. Below Tsp liquid properties cannot be
extrapolated, in line with Kauzmann's scenario of a `lower metastability limit'
of supercooled liquids as a solution of Kauzmann's paradox. The off-equilibrium
dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal
droplets, followed by extremely slow growth, due to the presence of pinning
energy barriers. In the early time region, which is longer the lower the
temperature, this crystal-growth phase is indistinguishable from an
off-equilibrium glass, both from a structural and a dynamical point of view:
crystal growth has not advanced enough to be structurally detectable, and a
violation of the fluctuation-dissipation theorem (FDT) typical of structural
glasses is observed. On the other hand, for longer times crystallization
reaches a threshold beyond which crystal domains are easily identified, and FDT
violation becomes compatible with ordinary domain growth.
