Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order
Different types of the lattice spin systems with the competing interactions have rich and interesting phase diagrams. In this study a system with competing nearest-neighbor interaction J1, prolonged next-nearest-neighbor interaction Jp and ternary prolonged interaction Jtp is considered on a Cayley...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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World Scientific Publishing Company
2012
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| Online Access: | http://irep.iium.edu.my/24304/1/S0129183112500398.pdf |
| _version_ | 1825646624704036864 |
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| author | Uguz, Selman Ganikhodjaev, Nasir Akin, Hasan Temir, Seyit |
| author_facet | Uguz, Selman Ganikhodjaev, Nasir Akin, Hasan Temir, Seyit |
| author_sort | Uguz, Selman |
| collection | IIUM |
| description | Different types of the lattice spin systems with the competing interactions have rich and interesting phase diagrams. In this study a system with competing nearest-neighbor interaction J1, prolonged next-nearest-neighbor interaction Jp and ternary prolonged interaction Jtp is considered on a Cayley tree of arbitrary order k. To perform this study, an iterative scheme is developed for the corresponding Hamiltonian model. At finite temperatures several interesting properties are presented for typical values of α = T/J1, β = −Jp/J1 and γ = -Jtp/J1. This study recovers as particular cases, previous work by Vannimenus1 with γ = 0 for k = 2 and Ganikhodjaev et al.2 in the presence J1, Jp, Jtp with k = 2. The variation of the wavevector q with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of our iterative system are studied in detail. |
| first_indexed | 2024-03-05T23:05:21Z |
| format | Article |
| id | oai:generic.eprints.org:24304 |
| institution | International Islamic University Malaysia |
| language | English |
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| publishDate | 2012 |
| publisher | World Scientific Publishing Company |
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| spelling | oai:generic.eprints.org:243042012-06-11T01:49:34Z http://irep.iium.edu.my/24304/ Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order Uguz, Selman Ganikhodjaev, Nasir Akin, Hasan Temir, Seyit QA Mathematics QC Physics Different types of the lattice spin systems with the competing interactions have rich and interesting phase diagrams. In this study a system with competing nearest-neighbor interaction J1, prolonged next-nearest-neighbor interaction Jp and ternary prolonged interaction Jtp is considered on a Cayley tree of arbitrary order k. To perform this study, an iterative scheme is developed for the corresponding Hamiltonian model. At finite temperatures several interesting properties are presented for typical values of α = T/J1, β = −Jp/J1 and γ = -Jtp/J1. This study recovers as particular cases, previous work by Vannimenus1 with γ = 0 for k = 2 and Ganikhodjaev et al.2 in the presence J1, Jp, Jtp with k = 2. The variation of the wavevector q with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of our iterative system are studied in detail. World Scientific Publishing Company 2012-06 Article PeerReviewed application/pdf en http://irep.iium.edu.my/24304/1/S0129183112500398.pdf Uguz, Selman and Ganikhodjaev, Nasir and Akin, Hasan and Temir, Seyit (2012) Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order. International Journal of Modern Physics C, 23 (5). 1250039 (1)-1250039 (15). ISSN 1793-6586 (O), 0129-1831 (P) http://www.worldscinet.com/ijmpc/23/2305/S0129183112500398.html 10.1142/S0129183112500398 |
| spellingShingle | QA Mathematics QC Physics Uguz, Selman Ganikhodjaev, Nasir Akin, Hasan Temir, Seyit Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order |
| title | Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order |
| title_full | Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order |
| title_fullStr | Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order |
| title_full_unstemmed | Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order |
| title_short | Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order |
| title_sort | lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/24304/1/S0129183112500398.pdf |
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