  We present here new evidence that after a quench the planar Potts model on
the square lattice relaxes towards a glassy state if the number of states q is
larger than four. By extrapolating the finite size data we compute the average
energy of these states for the infinite system with periodic boundary
conditions, and find that it is comparable with that previously found using
fixed boundary conditions. We also report preliminary results on the behaviour
of these states in the presence of thermal fluctuations
