For example we could take Zd, the set of points in Rdall of whose coordinates are integers. /Type /Annot In the Ising model spins have only two possible states ±1 (up or down). << /Contents 121 0 R /Title (Structure learning of antiferromagnetic Ising models) endobj /Type (Conference Proceedings) /D [34 0 R /XYZ 48.086 632.003 null] 41 0 obj << 7 0 obj ����)�2-�BC��3C��fPb��u���$TG�1fY���b>z�? 46 0 obj << endobj /F 4/Border[0 0 0]/H/I/C[0 1 0] /Filter /FlateDecode temperature of the 2d ferromagnetic Ising model is obtained using finite. >> endobj >> Antiferromagnetic Ising Model in the Framework of Riemannian Geometry 1827 and the relation between and the temperature slightly below the Néel temperature(T N) isapproximatelywrittenas[24] 2 3 (z 1) 2 = J k BT N; (8) where = T N T T N is the distance from the Néel temperature. /firstpage (2852) /Parent 1 0 R /Parent 1 0 R /Length 2519 (2.1 Description of the model and magnetic Gibbs energyin the Bethe approximation) /Parent 1 0 R /MediaBox [ 0 0 612 792 ] /Parent 1 0 R /ProcSet [ /PDF /Text ] 42 0 obj << 12 0 obj /Resources 122 0 R << /Filter /FlateDecode >> The antiferromagnetic Ising model has a negative interaction parameter, whereby neighbor- ing nodes prefer to be in opposite states. Consider a set Λ of lattice sites, each with a set of adjacent sites (e.g. a square lattice. /Published (2014) /Created (2014) /Rect [135.003 63.529 147.842 72.577] stream /A << /S /GoTo /D (cite.Felice) >> (1 Introduction) All three fundamental models can be realized with the generic Hamiltonian: for the Ising model, for the XY model and for the Heisenberg model. /Parent 1 0 R tz���c����VZ�Jf=��|�/ؘHNhV�X%�~���;�/ؔ�]q��+��n�R��d(X���&D4.601�P �XO�G�ؘ�e�Db !H�d�c+mG���Q���\B�����:�cvn!����@���L䟇0�5#Mv��T�'��}CG�����4bJ�i�&�{����栭&�!pp,�J�)��`:1ݜ݂E`����߶��,ܠ�e�+gc��qD�O����+��S�H�T��� T==7B�� |���c�dO�CM^��/�z\���@�oc,��se�E�����0 ��p!��^N /MediaBox [ 0 0 612 792 ] >> 20 0 obj endobj endobj '��ve|2�ZG����0B �A+O~_���ܸY�THd$u��'*�^/��),ϒ��O��_��W�\]G���H.��X'��w�#!�@�g����\����3F᪹ �ҳy&b' s�\��]_�h]�=���d.�˳剌�Q 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 to test Monte Carlo methods developed to tackle such problems. 39 0 obj << << /F 4/Border[0 0 0]/H/I/C[0 1 0] the influence of an external magnetic field are described. /Pages 1 0 R >> 1 0 obj 86 0 obj << (3.1 Riemannian geometry of a thermodynamic state space) /Subtype /Link /Subtype /Link size scaling. /Resources 46 0 R >> endobj Although the net magnetization should be zero at a temperature of absolute zero, the effect of spin cantingoften causes a small net mag… endobj 40 0 obj << 8 0 obj endobj endobj /Resources 144 0 R /Subject (Neural Information Processing Systems http\072\057\057nips\056cc\057) >> it is the iteration per frame number. mag is "magnification". /Contents 208 0 R In two dimensions this is usually called the square lattice, in three the cubic lattice and in one dimension it is often refered to as a chain. << /S /GoTo /D [34 0 R /Fit] >> 12 0 obj Ising Interactions in a Tilted Optical Lattice The quantum Ising model is a paradigmatic model of magnetism, and an Ising chain is one of the simplest many-body systems to exhibit a quantum phase transi-tion. The ferromagnetic two-dimensional Ising model on a square lattice is a collection of spins S i,j on each node (i,j) of a … endobj /ModDate (D\07220141202154419\05508\04700\047) 10 0 obj 1 A.The internal energy of the system depends only on the spin product σ i σ j of neighboring particles and on their relative positions, . A spin configuration, σ = (σk)k ∈ Λ is an assignment of spin value to each lattice site. >> endobj xڝY�s�8�_�{Sfj�"%�]o.m����I'����v�q4�e�$�M��Ȓ����!�@���L�.��Z>{q�����*;[����ά�6�f����? << /Contents 210 0 R >> << 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. This links each pair of nearest neighbors. >> endobj /Resources 171 0 R >> /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) /Rect [345.506 203.628 352.922 212.676] /Subtype /Link /Book (Advances in Neural Information Processing Systems 27) `���wG�]���y���sic�JT�4���pS�m[ 3m! /Contents 47 0 R -�/./������/�>}{�����_DzuN���������Y\�]�=[^�8��'3 r /MediaBox [ 0 0 612 792 ] /Contents 100 0 R /A << /S /GoTo /D (cite.Brody) >> In our Ising model, each site i at continuous position on a triangular network is occupied by a particle of discrete spin σ i = ± 1, and each nearest-neighbor bond comprises a harmonic spring of stiffness K and relaxed length a; see Fig. 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. 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. << /MediaBox [ 0 0 612 792 ] /D [34 0 R /XYZ 49.086 245.288 null] /MediaBox [0 0 453.543 666.142] 51 0 obj << /Kids [ 4 0 R 5 0 R 6 0 R 7 0 R 8 0 R 9 0 R 10 0 R 11 0 R 12 0 R ] We study the ground state of a d-dimensional Ising model with both long-range dipole-like and nearest-neighbor ferromagnetic FM interactions. endobj >> << /S /GoTo /D (section.2) >> /Parent 1 0 R 2 0 obj /Resources 209 0 R /Filter /FlateDecode << /A << /S /GoTo /D (cite.Felice) >> endobj endobj 1); i.e., the effective antiferromagnetic interaction decays as the in-plane separation increases . The thermostat algorithm is used. 35 0 obj << /Rect [151.274 63.529 164.113 72.577] << /S /GoTo /D (subsection.3.2) >> Other popular antiferromagnetic models include the Potts or coloring model, and the hard-core model. 21 0 obj Antiferromagnetic spins ordering appears for negative temperature. /Count 9 /EventType (Poster) 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�]���