Behaviors of Phase Diagrams of an Ising Model on a Cayley Tree-Like Lattice: Rectangular Chandelier

Abstract

In this work, we study an Ising model on a new lattice type which we called Rectangular Chandelier, with competing nearest‐neighbor interactions J1, prolonged ternary interactions Jt and one‐level next‐nearest‐neighbor quinary interactions Jl1(5). We obtain the phase diagrams of the Ising model related to Hamiltonian system give above on a Rectangular Chandelier. The phase diagrams are presented in the Hamiltonian 3‐parameter space. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1, Jt and Jl1(5). At finite temperatures several interesting features are exhibited for typical values of −Jt/J1. For some values of −Jt/J1 and Jl1(5)/J1/J1, we determine the existince of multicritical Lifshitz points that are at non zero temperature, while it was stuck at zero temperature T for all systems with competing interactions, studied on the Cayley tree in the previous works.