Antiferromagnetic clock models in two dimensions

Antiferromagnetic and asymmetric p-state clock models on a square lattice are analyzed with the renormalization group, by studying the effect of p-fold symmetry-breaking fields in the planar model. For p odd and {≥}3 ($p=3$ is the three-state Potts model) these models exhibit two phase transitions with a critical line of continuously varying exponent η(ηₘᵢₙ<η<1/4) separating them. When the couplings are antiferromagnetic in one direction only, ηₘᵢₙ=2p², while for the isotropic case ηₘᵢₙ=1p². In the latter case, the low-temperature phase is characterized by a $2p$-fold degeneracy.