Interrelations between various frustrated Ising and q-state models
M. Pleimling, B. Neubert and R. Siems
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
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 ANNNI- and DIS-parameters depends on
its precise form is given.
Conclusions regarding the influences of the mean field approximation for
the two models are discussed.