The Competing Interactions on a Cayley Tree-Like Lattice: Pentagonal Chandelier

• Authors: S. Uguz , N. Ganikhodjaev , H. Akin , S. Temir
• Languages of publication: EN

Abstracts

EN

Different types of lattice spin systems with competing interactions have rich and interesting phase diagrams. In this study we present some new results for such systems involving the Ising spin system (i.e. σ = ± 1) using a generalization of the Cayley tree-like lattice approximation. We study the phase diagrams for the Ising model on a Cayley tree-like lattice, a new lattice type called pentagonal chandelier, with competing nearest-neighbor interactions J_1, prolonged next-nearest-neighbor interactions J_{p} and one-level next-nearest-neighbor senary interactions J_{l_1}^{(6)}. The colored phase diagrams contain some multicritical Lifshitz points that are at nonzero temperature and many modulated new phases. We also investigate the variation of the wave vector with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of the system.

Keywords

EN

05.50.+q; 64.60.-i; 64.60.De

Discipline

• 64.60.De: Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.)
• 64.60.-i: General studies of phase transitions(see also 63.70.+h Statistical mechanics of lattice vibrations and displacive phase transitions; for critical phenomena in solid surfaces and interfaces, and in magnetism, see 68.35.Rh, and 75.40.-s, respectively)
• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 1
• Pages: 114-118

Dates

published

2012-01

Contributors

author

S. Uguz

• Arts and Science Faculty, Department of Mathematics, Harran University, Sanliurfa, 63120, Turkey

author

N. Ganikhodjaev

• Department of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia

author

H. Akin

• Faculty of Education, Department of Mathematics, Zirve University, Gaziantep, 27260, Turkey

author

S. Temir

• Arts and Science Faculty, Department of Mathematics, Harran University, Sanliurfa, 63120, Turkey

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Identifiers

DOI

10.12693/APhysPolA.121.114