>> endobj ο�0����,�E��p�i'�M�ݗ�ڊ?~�f ۔�U( ?WL�Qu�8��\�DD�pu^XK��Tx��gC��P� �SS}�;SH§"���8��x$��H�X�|J>ʟ���%������]�7%dž���(�,P�>�".�+D|�aj�e��]OD���/�� Hw� S��0�v >> /Subtype /Link We study the two-dimensional antiferromagnetic Ising model with a purely imaginary magnetic field, which can be thought of as a toy model for the usual θ physics. 28 0 obj /MediaBox [0 0 453.543 666.142] • Each lattice site has a single spin variable: s i = ±1. /Subtype /Link [>�?#��+ endobj endobj /Parent 1 0 R In an external magnetic field, a kind of ferrimagnetic behavior may be displayed in the antiferromagnetic phase, with the absolute value of one of the sublattice magnetizations differing from that of the other sublattice, resulting in a nonzero net magnetization. 12 0 obj 8 0 obj Choose 1024x1024 lattice. endobj %���� endobj << Antiferromagnetic Ising Model in the Framework of Riemannian Geometry 1827 and the relation between and the temperature slightly below the Néel temperature(T N) isapproximatelywrittenas[24] 2 3 (z 1) 2 = J k BT N; (8) where = T N T T N is the distance from the Néel temperature. 20 0 obj >> endobj /A << /S /GoTo /D (cite.Ruppeiner7) >> /Contents 13 0 R << /S /GoTo /D (subsection.2.1) >> << The H -dependence of two-spin correlations is calculated for a cluster of nine spins. ferromagnetic and antiferromagnetic Ising models on a square lattice are. /Rect [345.506 203.628 352.922 212.676] mag is "magnification". stream endobj << /Type /Page << /S /GoTo /D (section.4) >> >> /Font << /F22 49 0 R /F59 50 0 R /F19 52 0 R /F20 53 0 R /F23 54 0 R /F24 55 0 R /F14 56 0 R /F11 57 0 R /F7 58 0 R /F10 59 0 R /F8 60 0 R /F12 61 0 R /F13 62 0 R /F56 63 0 R /F57 64 0 R /F17 65 0 R >> We focus for simplicity on the classical Ising model, though our techniques apply to more general spin systems including the antiferromagnetic Potts model (colorings) and the hard-core model (independent sets). << 1. We study the ground state of a d-dimensional Ising model with both long-range dipole-like and nearest-neighbor ferromagnetic FM interactions. >> endobj *��j��r�`��$ʫ5}ȩi�vu���\KõoVuqST� ��Ϊ3-������[_׻m��|��.PW��܅U�=�����-�B�2Zvׅ��UU �� ) ��;4�=" �4d�U��h�]��h��s{���^g`��͑�?�,�i�M�؂ �A�yY��E�l}�m���;�|��D���,n�Ⱕ/�������8\Uo�8i����m�W��Ӊ͵���6 Z�|���I��I5F��v��z"leq�莠s#�����GC�%�����4 ���e��o��(�f�qv ��1��A(b9!e+aGR� �IkśT������H_�,�DT@��Qqی��H~m�S�[g�| :��{�w�UǙ�8q ߣ�����Aq� W���_��+����bCZ��v�+�B'Uw����n_��4s��y��TC>���!0�� o��������p�R��Z2 /D [34 0 R /XYZ 48.086 632.003 null] endobj /Parent 1 0 R /Subtype /Link (2.1 Description of the model and magnetic Gibbs energyin the Bethe approximation) /Type /Page x��Ɏ$Gr���!����dƒ� A�¡ �� �9����twq�I�A����E���o�TVJ�CeG����������O�_���v}�?����~x�~ݾo�ݩ=�O��~h�����޾������۾ۏ����a8���= ���]��ݯ]۵w߷ߴ��~�iw�}������RO~֣�7��p�o�v�6�z}������=����o��>k4ڏ���7�ۻm���t�� v����v`U��EY��2���D�pӸ���]�H�`ֿ3�_&%���?-Dע����:��S|���E���|h�f�NVKffwط/���wn�]��� question. According to the Mermin–Wagner theorem [ 4 ], no magnetic ordering is possible at any nonzero temperature in 1D or 2D isotropic Heisenberg models. /Subtype /Link classical Monte Carlo algorithm of Metropolis. << /S /GoTo /D (section.1) >> %PDF-1.4 (3.2 Thermodynamic curvature scalar for the antiferromagnetic Ising model) stream << 4 0 obj /Filter /FlateDecode (2.2 Magnetic Gibbs energy minimization and solutions at equilibrium) /Resources 171 0 R Our motivation is to have a benchmark calculation in a system which suffers from a strong sign problem, so that our results can be used t … 4 0 obj /A << /S /GoTo /D (cite.Brody) >> The critical . 1. /F 4/Border[0 0 0]/H/I/C[0 1 0] A spin configuration, σ = (σk)k ∈ Λ is an assignment of spin value to each lattice site. 1 0 obj /Parent 1 0 R 32 0 obj >> 40 0 obj << 38 0 obj << /F 4/Border[0 0 0]/H/I/C[0 1 0] Antiferromagnetic Ising Model in the Framework of Riemannian Geometry 1827 and the relation between and the temperature slightly below the Néel temperature(T N) isapproximatelywrittenas[24] 2 3 (z 1) 2 = J k BT N; (8) where = T N T T N is the distance from the Néel temperature. endobj /Resources 144 0 R endobj endobj endobj >> /Type /Catalog 51 0 obj << endobj /A << /S /GoTo /D (cite.Janyszek) >> /F 4/Border[0 0 0]/H/I/C[0 1 0] /Editors (Z\056 Ghahramani and M\056 Welling and C\056 Cortes and N\056D\056 Lawrence and K\056Q\056 Weinberger) /Contents 47 0 R 6 0 obj a graph) forming a d-dimensional lattice. /Type /Annot Consider a set Λ of lattice sites, each with a set of adjacent sites (e.g. Although the net magnetization should be zero at a temperature of absolute zero, the effect of spin cantingoften causes a small net mag… A number of two and four-spin correlation functions of the antiferromagnetic Ising model is explicitly calculated starting from the exact solution of the model. /Parent 1 0 R 24 0 obj For each lattice site k ∈ Λ there is a discrete variable σk such that σk ∈ {+1, −1}, representing the site's spin.

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