Phase diagrams of competing quadruple and binary interactions on Cayley tree-like lattice: Triangular Chandelier

We study the phase diagrams for the Ising model on a Cayley tree-like lattice, called Triangular Chandelier, with competing nearest-neighbour interactions J1, prolonged next-nearest-neighbour interactions Jp and one-level next-nearest-neighbour quadruple interactions Jl1. The phase diagrams display the multicritical points (the Lifshitz points) that are at nonzero temperature and many modulated phases. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular case, previous work of Vannimenus extension result given by Ganikhodjaev and Uğuz for k=3. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1,Jp and Jl1. At finite temperatures several interesting features are exhibited for typical values of Jl1/J1 and −Jp/J1.