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

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-neares...

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Bibliographic Details
Main Authors: Ganikhodjaev, Nasir, Zakaria, Siti Fatimah
Format: Article
Language:English
Published: INSI Publications 2011
Subjects:
Online Access:http://irep.iium.edu.my/7136/
http://irep.iium.edu.my/7136/
http://irep.iium.edu.my/7136/1/Paper_Ausr_173-181.pdf
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Summary: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.