Abstract
In the course of certification of the ANNNI model with the third nearest neighbour interaction J3 applied to the successive phase transitions occurring in the ferroelectric smectics the four body force J4b is shown to be induced. The effects of J3 and J4b are studied and J4b is shown not to be essential in the high temperature region in the ordered phases, which is applicable to the phase transitions concerned here. That means the first Hamiltonian is the effective Hamiltonian for these phenomena. The mesophases are studied where ferrielecric phase named as FIL is suggested to have a wave number 2/5, and those FIH and FI are assume to have the ones 2/7 and 1/5, respectively. The reasonwhy the mesophase FI is observed scarcely is also discussed on the basis of the phase diagrams.
