Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree - Ganikhodjaev, Nasir; Akin, Hasan; Uguz, Selman; Temir, Seyit (Eudoxus Press, LLC, 2011)
In this paper we consider the Ising model with spin values in Φ = {−1, 1}, the relevant Hamiltonian with competing binary nearest-neighbor, prolonged ternary and prolonged next-nearest neighbors interactions has the form H(σ) = −Jp >x,y< σ(x)σ(y) − Jt >x,¯y,z< σ(x)σ(y)σ(z)− J1 <x,y>σ(x)σ(y), where Jp, Jt, J1 ∈ R are coupling constants. We study the phase diagram of this model. 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 Jp. At finite temperatures several interesting features are exhibited for typical values of −Jt/J1 and Jp/J1.