On Ising Model with One-Level Pentagon Interactions on The Cayley Tree-Like Lattice: Pentagonal Chandelier

We study the phase diagrams for the Ising model that defined on Cayley tree-like lattice: pentagonal chandelier, with competing one-level pentagon interactions. Pentagonal chandelier can be viewed as another geometrical representation of Cayley tree order 5. The phase diagram was investigated for several ranges of the competing parameters and it showed the appearance of several features and modulated phase arising from the frustration effects introduced by the one-level pentagon interaction. The phase diagrams are obtained from stability conditions, and characteristic points in the iteration scheme are numerically analyzed. Lastly, the variation of wavevector with temperature in the modulated phase was studied in detail where narrow commensurate steps between incommensurate regions appeared when investigating the Lyapunov exponent associated with trajectory of the system.