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

• Main Authors: Ganikhodjaev, Nasir, Zakaria, Siti Fatimah
• Format: Book Chapter
• Language: English
• Published: Faculty of Engineering, International Islamic University Malaysia (IIUM) 2010
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf; http://irep.iium.edu.my/14382/

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