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-nearest...
| Main Authors: | , |
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| Format: | Book Chapter |
| Language: | English |
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Faculty of Engineering, International Islamic University Malaysia (IIUM)
2010
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/14382/ http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf |
| 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 |
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