INTERRELATIONS BETWEEN VARIOUS FRUSTRATED ISING-MODEL AND Q-STATE-MODEL

Hierarchical relations for q-state- and r-spin-models are discussed, A central role in this discussion is played by the Double Ising Spin (D IS) model with only nearest neighbor couplings, which was introduced f or a theoretical description of certain systems with uniaxially modula ted structures, It can be interpreted as a special four-state model. C ontinuing with the specialization, the four-state chiral clock model i s derived as a special case of the DIS model. Further more, it is show n that another particular DIS model can be mapped in an exact way onto the Axial Next Nearest Neighbor Ising (ANNNI) model. The relation con necting ANNNI- and DIS-parameters depends on temperature; its precise form is given, Conclusions regarding the influences of the mean field approximation for the two models are discussed.