  The ferromagnetic q-state Potts model on a square lattice is analyzed, for
q>4, through an elaborate version of the operatorial variational method. In the
variational approach proposed in the paper, the duality relations are exactly
satisfied, involving at a more fundamental level, a duality relationship
between variational parameters. Besides some exact predictions, the approach is
very effective in the numerical estimates over the whole range of temperature
and can be systematically improved.
