MULTICOMPONENT CHIRAL POTTS MODELS

It is shown that an (N_ρ,N_σ) chiral Potts model, which is a generalization of the Ashkin-Teller model and consists of two chiral Potts models which are coupled together by four-spin interactions, can always be mapped to a single chiral Potts model of N_ρN_σ states if N_ρ and N_σ are relative prime. Moreover, if on every lattice site there are d spins with N_ρ,…,N_σ states, respectively, similar mappings exist: If there are chiral two-spin interactions between nearest neighbor spins of the same kind and if the d sublattices are coupled together by chiral 2j-spin interactions for j≤d between the j pairs of spins, this defines a composite (N_ρ,…,N_σ) state chiral Potts model. If (N_i,N_j)=1, for i≠j, i,j=1,…,d, then the composite model with (N_ρ,…,N_σ) states can be mapped into a -state chiral Potts model. Finally, it is shown that if one or more of the spins of a unit cell sits on the dual lattice whereas the other spins sit on the original lattice, so that this is a generalization of the eight-vertex model in the spin language, such a mapping also exists. This mean that results obtained for the chiral Potts models can be used for many such composite models.