48 0 obj (2 Evolution of magnetization profiles) << /D (section*.11) /S /GoTo >> endobj 21 0 obj endobj To summarize, we have studied the isotropic biquadratic Heisenberg model in two and three dimensions for negative u. (A Ground state energy, the gap, and the temperature) 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. endobj << /D (section*.17) /S /GoTo >> 32 0 obj 53 0 obj << /D [ 74 0 R /Fit ] /S /GoTo >> (Abstract) 9 0 obj %� endstream Conditions and any applicable 56 0 obj (3 Short-time wavepacket pinch) It admits several integrable and nonintegrable generalizations like Landau-Lifshitz equation, Ishimori equation and so on. 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*.13) /S /GoTo >> << /D (section*.18) /S /GoTo >> Agreement. 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. Exact results in one dimension are also obtained for the partition function and susceptibility of a "planar" classical Heisenberg model. 33 0 obj 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. Mz�5qX&�,�? << /D (section*.10) /S /GoTo >> 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. << /D (section*.5) /S /GoTo >> << /D (section*.3) /S /GoTo >> endobj 45 0 obj endobj Learn More », Sign up to receive regular email alerts from Physical Review Journals Archive. (B Methods) endobj (Finite-temperature magnetization transport of the one-dimensional anisotropic Heisenberg model) 20 0 obj endobj endobj Buy the print book Check if you have access via personal or institutional login. endobj 52 0 obj 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. The anisotropy however, produces long-range order. 65 0 obj 17 0 obj Chapter. (II Model and methods) (I Introduction) In this model the spin vectors interact via a Heisenberg coupling but each spin vector is restricted to lie in a plane. 57 0 obj It is related to the prototypical Ising model, where at each site of a lattice, a spin << /D (section*.9) /S /GoTo >> Log … << /D (section*.7) /S /GoTo >> 28 0 obj endobj << /D (section*.12) /S /GoTo >> The isotropic Heisenberg model; Thermodynamics of One-Dimensional Solvable Models. endobj 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. 3 0 obj 29 0 obj (C Master equation setting) 40 0 obj endobj endobj 16 0 obj 69 0 obj Use of the American Physical Society websites and journals implies that In the two-dimensional Heisenberg model the order is absent at T ≠ 0 (see, for instance, Patashinskii and Pokrovsky, 1979). (V Conclusion) 24 0 obj endobj endobj endobj Chapter; Aa; Aa; Get access. ]=�vC�����{�`��w؎Ͱ�m��&N�d�C����$���O~��"�dl~��e��a�$wq��Rx����S��v֩j�������4 ���05��_"�p�6 (B Localized packets) 41 0 obj ( Acknowledgments) 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. endobj << /D (section*.14) /S /GoTo >> endobj %���� 44 0 obj endobj In two dimensions, we have identified the intermediate phase as the quadrupolar phase. 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. %PDF-1.4 endobj <>stream Subscription All rights reserved. Thermodynamics of One-Dimensional Solvable Models. 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. 110 0 obj xڍ[[��6�~ϯ�G�� �����gs;��df6������! 68 0 obj 60 0 obj The results are compared briefly with those for Ising and Heisenberg chains of spin 1 2. );���[_U�"%�&n� the user has read and agrees to our Terms and The values of the magnetizations have been underlined near the related curve. endobj (A Model) endobj 25 0 obj endobj It is found that the perturbation series for the energy per spin breaks down as T→0. (III Transport properties) 8 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���. 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. 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� endobj (IV Domain wall dynamics) << /Filter /FlateDecode /Length 5115 >> 61 0 obj 36 0 obj 4 0 obj endobj 72 0 obj 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 … ( References) Information about registration may be found here. 73 0 obj endobj endobj 37 0 obj This equation is called the continuous classical Heisenberg ferromagnet equation or shortly Heisenberg model and is integrable in the sense of soliton theory. endobj endobj << /D (section*.15) /S /GoTo >> << /D (section*.16) /S /GoTo >> 12 0 obj endobj << /D (section*.4) /S /GoTo >> ©2020 American Physical Society. 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" << /D (section*.1) /S /GoTo >> 13 0 obj <. endobj 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. endobj The phase transition at a finite temperature has been excluded. << /D (section*.6) /S /GoTo >> endobj 2 0 obj %PDF-1.4 Detailed calculations are performed to third order in γ−1. << /D (section*.8) /S /GoTo >> This series is rearranged to give a simplified diagram expansion. 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. 5 0 obj (4 Magnetization offset B0) 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. 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� 64 0 obj 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. endobj (1 Preparation of initial states) 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 ». endobj stream 49 0 obj endobj endobj ISSN 1536-6065 (online).