Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree
In this paper we consider the Ising model with spin values in Φ = {−1, 1}, the relevant Hamiltonian with competing binary nearest-neighbor, prolonged ternary and prolonged next-nearest neighbors interactions has the form H(σ) = −Jp �� >x,y< σ(x)σ(y) − Jt >x�,¯y,z< σ(x)σ(y)σ(z)− J1 � &l...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Eudoxus Press, LLC
2011
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| Online Access: | http://irep.iium.edu.my/1688/ http://irep.iium.edu.my/1688/1/Phase_diagrams_of_an_ising_system_with_competing_binary%2C_prolonged.pdf |
| _version_ | 1848775900306341888 |
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| author | Ganikhodjaev, Nasir Akin, Hasan Uguz, Selman Temir, Seyit |
| author_facet | Ganikhodjaev, Nasir Akin, Hasan Uguz, Selman Temir, Seyit |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | In this paper we consider the Ising model with spin values in Φ = {−1, 1}, the relevant Hamiltonian with competing binary nearest-neighbor, prolonged ternary and prolonged next-nearest neighbors interactions has the form
H(σ) = −Jp �� >x,y< σ(x)σ(y) − Jt >x�,¯y,z<
σ(x)σ(y)σ(z)− J1 � <x,y>σ(x)σ(y),
where Jp, Jt, J1 ∈ R are coupling constants. We study the phase diagram of this model. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1, Jt and Jp. At finite temperatures several interesting features are exhibited for typical values of −Jt/J1 and Jp/J1. |
| first_indexed | 2025-11-14T14:21:32Z |
| format | Article |
| id | iium-1688 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:32Z |
| publishDate | 2011 |
| publisher | Eudoxus Press, LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-16882011-12-13T08:45:54Z http://irep.iium.edu.my/1688/ Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree Ganikhodjaev, Nasir Akin, Hasan Uguz, Selman Temir, Seyit QA Mathematics QC Physics In this paper we consider the Ising model with spin values in Φ = {−1, 1}, the relevant Hamiltonian with competing binary nearest-neighbor, prolonged ternary and prolonged next-nearest neighbors interactions has the form H(σ) = −Jp �� >x,y< σ(x)σ(y) − Jt >x�,¯y,z< σ(x)σ(y)σ(z)− J1 � <x,y>σ(x)σ(y), where Jp, Jt, J1 ∈ R are coupling constants. We study the phase diagram of this model. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1, Jt and Jp. At finite temperatures several interesting features are exhibited for typical values of −Jt/J1 and Jp/J1. Eudoxus Press, LLC 2011-01 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1688/1/Phase_diagrams_of_an_ising_system_with_competing_binary%2C_prolonged.pdf Ganikhodjaev, Nasir and Akin, Hasan and Uguz, Selman and Temir, Seyit (2011) Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree. Journal of Concrete and Applicable Mathematics, 9 (1). pp. 26-34. ISSN 1559-176X (O), 1548-5390 (P) http://www.ccs2012.org/files/2010/ccs2010_4_JCAAM--VOL-9--2011--NO--1.pdf |
| spellingShingle | QA Mathematics QC Physics Ganikhodjaev, Nasir Akin, Hasan Uguz, Selman Temir, Seyit Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree |
| title | Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree |
| title_full | Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree |
| title_fullStr | Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree |
| title_full_unstemmed | Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree |
| title_short | Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree |
| title_sort | phase diagrams of an ising system with competing binary, prolonged ternary and next-nearest interactions on a cayley tree |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/1688/ http://irep.iium.edu.my/1688/ http://irep.iium.edu.my/1688/1/Phase_diagrams_of_an_ising_system_with_competing_binary%2C_prolonged.pdf |