On some dynamic systems arising in lattice models with competing ternary interactions

The lattice models on a Cayley tree with competing interactions has recently been studied extensively because of the appearance of nontrivial magnetic orderings [1]. In the case of the Ising model on the Cayley tree of second order with competing binary nearestneighbour interactions J and binary prolonged second neighbour interactions Jp Vannimenus [1] was able to find new modulated phases, in addition to the expected paramagnetic and ferromagnetic phases. Later similar result was proved for Potts model with three spins [2]. Let Le