Interrelations between various frustrated Ising- and q-state-models

Abstract

Hierarchical relations for q-state- and r-spin-models are discussed. A central role in this discussion is played by the Double Ising Spin (DIS) model with only nearest neighbor couplings, which was introduced for a theoretical description of certain systems with uniaxially modulated structures. It can be interpreted as a special four-state model. Continuing with the specialization, the four-state chiral clock model is derived as a special case of the DIS model. Furthermore, it is shown that another particular DIS model can be mapped in an exact way onto the Axial Next Nearest Neighbor Ising (ANNNI) model. The relation connecting ANNNIand 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.