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

• Main Authors: Ganikhodjaev, Nasir, Zakaria, Siti Fatimah
• Format: Conference or Workshop Item
• Language: English
• Published: 2010
• Subjects: QA Mathematics; QC Physics
• Online Access: http://irep.iium.edu.my/1743/2/ICMAE2010-SITI_FATIMAH.pdf; http://irep.iium.edu.my/1743/

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 so-called antiphase with period 4 only.