isotropic heisenberg model

A high-temperature series expansion for the anisotropic model, which is valid for a general interaction potential and lattice, is derived by generalizing the methods developed by Horwitz and Callen for the Ising model. 72 0 obj Chapter. stream endobj endobj endobj 73 0 obj 16 0 obj 21 0 obj << /D (section*.13) /S /GoTo >> Mz�5qX&�,�? << /D (section*.17) /S /GoTo >> endobj (2 Evolution of magnetization profiles) Conditions and any applicable x�}V]S�0�g��{���X�d����:��/LbJ������=9��l�'�,�j��N�,��"0gy��u�#}+�Q�`�p%�U$a_MyPO�ι �!���]�Z�Q8�q���L� c� << /D (section*.12) /S /GoTo >> endobj Use of the American Physical Society websites and journals implies that Agreement. Information about registration may be found here. 61 0 obj The results are compared briefly with those for Ising and Heisenberg chains of spin 1 2. (A Model) It admits several integrable and nonintegrable generalizations like Landau-Lifshitz equation, Ishimori equation and so on. n���ܳ���xpڃ�\�'9�|�~ ��Sg�g�5� ��.&*Ů�W��x���~��3�q��q��qj��qj��q&>���� Q��z=3�.U\L��w���&ء�jj莪��V�6h�H�Ӭ��̈��kZ�yOs�K��%f+;�if�+�6��#��+�!B�+D\��1f���V�����h���Q�dM���������]K���f�)�3���MAm��؁���^k^�o�Y+DTI� �Ħy_�[��Jl:��t��9���K&��r����u��dh%n�o���į~3�B�#�+�c:���ኑ����Y�m��B�n��D+8Za�C+���R��W {�+{O:��m�Ƶ����c3�1�kЦ�i�k��Q�g� %PDF-1.4 36 0 obj << /D (section*.16) /S /GoTo >> << /D (section*.18) /S /GoTo >> It is related to the prototypical Ising model, where at each site of a lattice, a spin (III Transport properties) Subscription <. endobj ( Acknowledgments) All rights reserved. ( References) << /D (section*.7) /S /GoTo >> 37 0 obj endobj << /D (section*.14) /S /GoTo >> 60 0 obj <>stream 3 0 obj endobj The isotropic Heisenberg model; Thermodynamics of One-Dimensional Solvable Models. 110 0 obj It is found that the perturbation series for the energy per spin breaks down as T→0. endobj endobj << /Filter /FlateDecode /Length 5115 >> 68 0 obj endobj Log … << /D [ 74 0 R /Fit ] /S /GoTo >> (I Introduction) %PDF-1.4 endobj (Finite-temperature magnetization transport of the one-dimensional anisotropic Heisenberg model) 56 0 obj 25 0 obj (B Localized packets) It is shown that the methods used to derive these results enable the partition functions and susceptibilities of finite clusters of interacting classical spins to be evaluated in terms of the 3n−j symbols of Wigner. 28 0 obj 5 0 obj 13 0 obj << /D (section*.15) /S /GoTo >> 57 0 obj 45 0 obj endobj << /D (section*.1) /S /GoTo >> endobj Detailed calculations are performed to third order in γ−1. ©2020 American Physical Society. endobj The values of the magnetizations have been underlined near the related curve. This series is rearranged to give a simplified diagram expansion. 49 0 obj To summarize, we have studied the isotropic biquadratic Heisenberg model in two and three dimensions for negative u. endobj Exact results in one dimension are also obtained for the partition function and susceptibility of a "planar" classical Heisenberg model. Equally valued magnetization curves of the isotropic Heisenberg model in a (kBT / J − r1) plane with the film thickness values (a) L = 3 and (b) L = 10 and r2 = 1.0. (C Master equation setting) u�� Gw���"����Wzk�;c�2M�݇ǻ< m����,�������m�֣ێ�����&p}5�{G�< Nաuc�����W� ]�~Z��mG׵n��O�6[��jc�Fڪ�fj7��S���χ�ݙ" Learn More », Sign up to receive regular email alerts from Physical Review Journals Archive. (3 Short-time wavepacket pinch) (II Model and methods) (B Methods) The anisotropy however, produces long-range order. << /D (section*.8) /S /GoTo >> ]=�vC�����{�`��w؎Ͱ�m��&N�d�C����$���O~��"�dl~��e��a�$wq��Rx����S��v֩j�������4 ���05��_"�p�6 12 0 obj 40 0 obj 9 0 obj endobj endobj This equation is called the continuous classical Heisenberg ferromagnet equation or shortly Heisenberg model and is integrable in the sense of soliton theory. Chapter; Aa; Aa; Get access. 20 0 obj �4�5^�������1��%� v�K��E�b���xYF~�qv�R�\�a�"�4|��d��8�+hWY�� q�wUD�����k�����ݹ��� 1��@rp"��ÙC(�G�o�O�����������j+�w]�t�\[W+;6Q��w�,� �̟?��w�0��y�0CF���. 17 0 obj endobj 8 0 obj (4 Magnetization offset B0) 53 0 obj endobj endobj The anisotropic classical Heisenberg model described by the Hamiltonian H=−Σ(ij)2(Jijxsixsjx+Jijysiysjy+Jijzsizsjz)−mHΣj=1Nsiz, where six, siy, and siz are components of the unit vector si, is also considered. The anisotropic classical Heisenberg model described by the Hamiltonian H=−Σ(ij)2(Jijxsixsjx+Jijysiysjy+Jijzsizsjz)−mHΣj=1Nsiz,where six, siy, and sizare components of the unit vector si, is also considered. endstream In 1931 Hans Bethe attempted to solve the many-body interaction model of the 1D isotropic Heisenberg spin-1/2 chain, and predicted the existence of two-magnon bound states 1. << /D (section*.6) /S /GoTo >> endobj 65 0 obj 24 0 obj In two dimensions, we have identified the intermediate phase as the quadrupolar phase. << /D (section*.5) /S /GoTo >> 2 0 obj (1 Preparation of initial states) endobj The isotropic Heisenberg model is a magnetic model in which interaction energy of spins s1 and s2 on the neighboring sites of the lattice is equal to Js1 •s2. << /D (section*.4) /S /GoTo >> The Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. 33 0 obj The phase transition at a finite temperature has been excluded. Buy the print book Check if you have access via personal or institutional login. ISSN 1536-6065 (online). 44 0 obj endobj Thermodynamics of One-Dimensional Solvable Models. (Abstract) endobj << /D (section*.3) /S /GoTo >> Physical Review™, Physical Review Letters™, Physical Review X™, Reviews of Modern Physics™, Physical Review A™, Physical Review B™, Physical Review C™, Physical Review D™, Physical Review E™, Physical Review Applied™, Physical Review Fluids™, Physical Review Accelerators and Beams™, Physical Review Physics Education Research™, APS Physics logo, and Physics logo are trademarks of the American Physical Society. 64 0 obj endobj << /D (section*.11) /S /GoTo >> endobj endobj endobj 69 0 obj %� 4 0 obj );���[_U�"%�&n� DOI:https://doi.org/10.1103/PhysRev.155.478, To celebrate 50 years of enduring discoveries, APS is offering 50% off APCs for any manuscript submitted in 2020, published in any of its hybrid journals: PRL, PRA, PRB, PRC, PRD, PRE, PRApplied, PRFluids, and PRMaterials. endobj 32 0 obj Physical Review Physics Education Research, Log in with individual APS Journal Account », Log in with a username/password provided by your institution », Get access through a U.S. public or high school library ». In this model the spin vectors interact via a Heisenberg coupling but each spin vector is restricted to lie in a plane. Exact expressions for the partition function, spin pair correlation function, and susceptibility of the onedimensional isotropic classical Heisenberg model are obtained in zero external field with cyclic boundary conditions. endobj (V Conclusion) (IV Domain wall dynamics) xڍ[[��6�~ϯ�G�� �����gs;��df6������! Finally, a practical technique for calculating the high-temperature series expansions of the zero-field free energy and susceptibility of the isotropic classical Heisenberg model is presented. << /D (section*.9) /S /GoTo >> endobj the user has read and agrees to our Terms and 29 0 obj In the two-dimensional Heisenberg model the order is absent at T ≠ 0 (see, for instance, Patashinskii and Pokrovsky, 1979). endobj endobj It is observed that the free-energy, susceptibility, and correlation functions for a linear chain of N spins with nearest-neighbor isotropic Heisenberg coupling can be calculated explicitly in the (classical) limit of infinite spin. %���� 41 0 obj endobj ʸ����1iJp ��(�Iw)3��u�f���W��ſ��C;�����Rʁs�{�����m�[#:Lw}^`Fo��k�1� g���Ǹ=��ߗhF9kןj�}�٭�-�]��!���=i�c�]l��T��P�!��G-���Gk�ΑL�����Q�mV� A perturbation series for the zero-field free energy of the anisotropic model in one dimension with nearest-neighbor interactions Jijx=Jijy=J and Jijz=γJ is developed in powers of γ−1 using the isotropic model as the unperturbed system. 48 0 obj endobj The Heisen- berg model, suggested3by W. Heisenberg in 1928, was initially proposed to explain a high phase transition tem- perature in ferromagnets that could not … (A Ground state energy, the gap, and the temperature) endobj 52 0 obj << /D (section*.10) /S /GoTo >>

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