Phase diagram of the Ising model with next-nearest-neighbour interactions

• Main Authors: Ganikhodjaev, Nasir, Zakaria, Siti Fatimah
• Format: Article
• Language: English
• Published: INSI Publications 2011
• Subjects: QA Mathematics; QC Physics
• Online Access: http://irep.iium.edu.my/7136/1/Paper_Ausr_173-181.pdf; http://irep.iium.edu.my/7136/; http://www.insipub.com/ajbas/2011/173-181.pdf

We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jp and one-level next-nearest neighbour interactions J0. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1 and prolonged next-nearest neighbour interactions Jp contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo … 0. For given lattice model on a Cayley tree, i.e., Jp … 0; Jo … 0 with J1 = 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1 and show that the class of modulated phases consists of socalled antiphase with period 4 only.