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We studied the non-equilibrium dynamics of the q-state Potts model in thesquare lattice, after a quench to sub-critical temperatures. By means of acontinuous time Monte Carlo algorithm (non-conserved order parameter dynamics)we analyzed the long term behavior of the energy and relaxation time for a widerange of quench temperatures and system sizes. For q>4 we found the existenceof different dynamical regimes, according to quench temperature range. At low(but finite) temperatures and very long times the Lifshitz-Allen-Cahn domaingrowth behavior is interrupted with finite probability when the system stuck inhighly symmetric non-equilibrium metastable states, which induce activation inthe domain growth, in agreement with early predictions of Lifshitz [JETP 42,1354 (1962)]. Moreover, if the temperature is very low, the system always getsstuck at short times in a highly disordered metastable states with finite lifetime, which have been recently identified as glassy states. The finite sizescaling properties of the different relaxation times involved, as well as theirtemperature dependency are analyzed in detail.

Long term ordering kinetics of the two dimensional q-state Potts model