Modulated Phase of an Ising System with Quinary and Binary Interactions on a Cayley Tree-like Lattice: Rectangular Chandelier

Selman Uğuz ； Hasan Akin

《Chinese Journal of Physics》 49卷3期 (2011/06) Pp. 788-801

並列摘要

In the present work we study the phase diagrams for the Ising model on a Cayley tree-like lattice, a new lattice type called a Rectangular Chandelier, with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions J(subscript p), and one-level next-nearest-neighbor quinary interactions J(superscript (5) subscript l1). The diagrams contain some multicritical Lifshitz points that are at nonzero temperature and many modulated new phases. This appears to shift the multicritical Lifshitz point to finite temperature, while it was stuck at zero temperature T for all systems with competing interactions in the previous works. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as a particular case, the previous work of the Vannimenus extension result given by Ganikhodjaev et al. for k=4. At vanishing temperature, the phase diagram is fully determined for all values and signs of the parameters J1, J(subscript p), and J(superscript (5) subscript l1). For some critical points, the variation of the wavevector with temperature in the modulated phase is also analyzed.