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Phase ordering and symmetries of the Potts model

We have studied the ordering of the q-colour Potts model in two dimensions on a square lattice. On the basis of our observations we propose that if q is large enough, the system is not able to break global and local null magnetization symmetries at zero temperature: when q<4 the system forms domains with a size proportional to the system size while for q > 4 it relaxes towards a non-equilibrium phase with energy larger than the ground state energy, in agreement with the previous findings of De Oliveira et al.