Ising model with restricted interactions on general Cayley tree of arbitrary order - Ganikhodjaev, Nasir; Zakaria, Siti Fatimah (INSI Publications, 2011)
We study an Ising model on a general Cayley tree with competing interaction of next-nearest-neighbour of two types; prolonged and one-level k-tuple interactions. Vannimenus covers a study of Ising model on competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interaction Jp. Later Mariz et al extend Vannimenus work by adding a one-level interaction Jo for order 2 with the existence of external magnetic field. And recently Ganikhodjaev et al found only simple modulated phases exist for Ising model with second neighbour prolonged and one-level competing interaction of order 2. So, in this paper, we study the Ising model with competing interaction J0≠0, Jp≠0 and J1=0 to identify the preservation of those phases for higher order k. We derived two types of general system of equations and describe the phase diagram for both cases of even and odd order.