Phase ordering and symmetries of the Potts model

Abstract

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.

Notes

^†There exists a fraction of realizations which fall to the ground state, but this fraction decreases very fast with L and it is negligible in the thermodynamic limit.

^‡In the numerical construction of γ, we have taken the nearest 24 neighbours of each site for the definition of the mentioned cell.