Year 2024,
Volume: 8 Issue: 2, 243 - 250, 31.12.2024
Ali Tozar
,
Orkun Taşbozan
,
Ali Kurt
References
-
[1] H.A. Zad, N. Ananikian, Phase transitions and magnetization of the mixed-spin Ising-
Heisenberg double sawtooth frustrated ladder, J. Phys.-Condes. Matter, 30 (2018) 9.
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Appl., 6 (1907) 661-690.
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636.
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[4] H.Y. Zou, R. Yu, J.D. Wu, Universality of Heisenberg-Ising chain in external fields, J.
Phys.-Condes. Matter, 32 (2020) 8.
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[5] H.A. Zad, N. Ananikian, R. Kenna, The specific heat and magnetic properties of two species
of spin-1/2 ladders with butterfly-shaped unit blocks, J. Phys.-Condes. Matter, 31 (2019) 11.
-
[6] H.A. Zad, M. Sabeti, A. Zoshki, N. Ananikian, Electrocaloric effect in the two spin-1/2
XXZ Heisenberg edge-shared tetrahedra and spin-1/2 XXZ Heisenberg octahedron with
Dzyaloshinskii-Moriya interaction, J. Phys.-Condes. Matter, 31 (2019) 11.
-
[7] D.V. Dmitriev, V.Y. Krivnov, Heisenberg-Ising delta-chain with bond alternation, J. Phys.-
Condes. Matter, 30 (2018) 8.
-
[8] T.A. Sulaiman, T. Akturk, H. Bulut, H.M.Baskonus, Investigation of various soliton solutions
to the Heisenberg ferromagnetic spin chain equation, Journal of Electromagnetic
Waves and Applications, 32 (2018) 1093-1105.
-
[9] H. Triki, A.M.Wazwaz, New solitons and periodic wave solutions for the (2+1)-dimensional
Heisenberg ferromagnetic spin chain equation, J Electromagn Waves Appl., 30 (2016) 788-
794.
-
[10] T. Anitha, M.M. Latha, C.C. Vasanthi, Dromions in (2+1)-dimensional ferromagnetic spin
chain with bilinear and biquadratic interactions, Physica A., 415 (2014) 105-115.
-
[11] M. Inc, I.E. Inan, Y. Ugurlu, New applications of the functional variable method, Optik,
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-
[12] Y. Cenesiz, O. Tasbozan, A. Kurt, Functional Variable Method for conformable fractional
modified KdV-ZK equation and Maccari system, Tbilisi Mathematical Journal, 10 (2017)
118-126.
-
[13] O. Tasbozan, N.M. Yagmurlu, A. Esen, The functional variable method for some nonlinear
(2+ 1)-dimensional equations, Selcuk Journal of Applied Mathematics, 14 (2013) 37-46.
Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation
Year 2024,
Volume: 8 Issue: 2, 243 - 250, 31.12.2024
Ali Tozar
,
Orkun Taşbozan
,
Ali Kurt
Abstract
The Heisenberg spin chain concept is a fundamental and generic model that describes the exotic magnetic behavior of certain materials, such as ferromagnetism, antiferromagnetism,
andferrimagnetism under critical temperatures. The concept of spin chain is based on Coulomb interactions due to Pauli exclusion principle rather than dipole-dipole interactions in explaining the high energy observed in the Weiss molecular field. With certain improvements to the Hamiltonian proposed by Heisenberg, the model has became more sophisticated and used successfully in explaining many of the physical phenomena observed experimentally. This model has been extensively studied by physicists since the emergence of quantum physics at the beginning of the 20th century. Due to nonlinear interactions inherent in the model, soliton solutions that can be obtained have attracted the attention of mathematicians, in recent decades. In this study, triangular soliton, bell shaped solitary wave and kink shaped solitary wave solutions were obtained by applying the functional variable method to the nonlinear Heisenberg spin chain equation for a cubic lattice crystal.
References
-
[1] H.A. Zad, N. Ananikian, Phase transitions and magnetization of the mixed-spin Ising-
Heisenberg double sawtooth frustrated ladder, J. Phys.-Condes. Matter, 30 (2018) 9.
-
[2] P.Weiss, L’hypoth`ese du champ mol´eculaire et la propri´et´e ferromagn´etique, J. Phys. Theor.
Appl., 6 (1907) 661-690.
-
[3] W. Heisenberg, Zur Theorie des Ferromagnetismus, Zeitschrift f¨ur Physik, 49 (1928) 619-
636.
-
[4] H.Y. Zou, R. Yu, J.D. Wu, Universality of Heisenberg-Ising chain in external fields, J.
Phys.-Condes. Matter, 32 (2020) 8.
-
[5] H.A. Zad, N. Ananikian, R. Kenna, The specific heat and magnetic properties of two species
of spin-1/2 ladders with butterfly-shaped unit blocks, J. Phys.-Condes. Matter, 31 (2019) 11.
-
[6] H.A. Zad, M. Sabeti, A. Zoshki, N. Ananikian, Electrocaloric effect in the two spin-1/2
XXZ Heisenberg edge-shared tetrahedra and spin-1/2 XXZ Heisenberg octahedron with
Dzyaloshinskii-Moriya interaction, J. Phys.-Condes. Matter, 31 (2019) 11.
-
[7] D.V. Dmitriev, V.Y. Krivnov, Heisenberg-Ising delta-chain with bond alternation, J. Phys.-
Condes. Matter, 30 (2018) 8.
-
[8] T.A. Sulaiman, T. Akturk, H. Bulut, H.M.Baskonus, Investigation of various soliton solutions
to the Heisenberg ferromagnetic spin chain equation, Journal of Electromagnetic
Waves and Applications, 32 (2018) 1093-1105.
-
[9] H. Triki, A.M.Wazwaz, New solitons and periodic wave solutions for the (2+1)-dimensional
Heisenberg ferromagnetic spin chain equation, J Electromagn Waves Appl., 30 (2016) 788-
794.
-
[10] T. Anitha, M.M. Latha, C.C. Vasanthi, Dromions in (2+1)-dimensional ferromagnetic spin
chain with bilinear and biquadratic interactions, Physica A., 415 (2014) 105-115.
-
[11] M. Inc, I.E. Inan, Y. Ugurlu, New applications of the functional variable method, Optik,
136 (2017) 374-381.
-
[12] Y. Cenesiz, O. Tasbozan, A. Kurt, Functional Variable Method for conformable fractional
modified KdV-ZK equation and Maccari system, Tbilisi Mathematical Journal, 10 (2017)
118-126.
-
[13] O. Tasbozan, N.M. Yagmurlu, A. Esen, The functional variable method for some nonlinear
(2+ 1)-dimensional equations, Selcuk Journal of Applied Mathematics, 14 (2013) 37-46.