Relations between two‐dimensional physical systems, continuous‐spin Hamiltonians, and discrete spin or Potts models are established by Landau symmetry and renormalization‐group arguments. Experimental realizations ofXYand Heisenberg models with cubic anisotropy as well as of different Potts models are reviewed. Then a unified model encompassing these classes of models is introduced. For the special case of a six‐state discrete model a phase diagram is proposed based on duality and Migdal renormalization‐group transformations.