�8�������HS��e? >> 84 0 obj /Filter /FlateDecode These lecture notes provide a detailed introduction to phase transitions and the /Font << /F23 6 0 R >> >> /Type /XObject 112 0 obj stream /Subtype /Form << The ground state was determined to be-36. /Parent 10 0 R I This procedure can be interpreted as coordinate descent in the m Permission is granted to copy and distribute freely, so long as proper Consider a system of half integer Ising spins with the Hamiltonian H = -JEơi dj -T -roiz where ir = - (); =(:-), This model was originally proposed by de Gennes (69) and has recently been much studied as a model for "quantum phase transitions” in systems such as LiHoF4 (see e.g. >> endobj 2 0 obj << Perimeter Institute Statistical Physics Lecture Notes part 7. stream 1 Introduction and Theory 1.1 The Ising Model The Ising model is a model used in statistical mechanics, typically to simulate magnetic systems. Though mean eld theory often leads to answers which differ from their actual values, it has always been the rst approach taken by reseachers to predict the phase diagrams. %PDF-1.5 æ��SZi��3�aJf�ێ�!��&�D��2œ��l��=�|����dfT��ʌ�'=�{���9�(3�������4���?K��Q27�Wq���e��;��G|��~���ګ{����8�)ܒk7�n_�;Ҥ�,��=I:��.�y[J�7IG� ��E�D׫�Ż��~�������o_�J�s"�2�� C���1�>c��"��s��B|����E����gA��o������vc:i_9?O��VT*-�tu!c��N�L��d��\l�zV6����}������������r�2��+��Z����}���f���I�����¡��/�x"���|T��m��z��Toj��=/�C�6��E5+�֞myQ4M��z�\��!ppe�9g������p���.ޘz��x��;*�Q>X�!p�������2�9U��e�[ޜG���s!�#���z۔�G�ຓģz���@@�f�j]wsuSn��v9������ͫ�3��M9��C2L�:&�i�:�(�/Þ��t=��s���l��"�u@�l��pE�{�8f� p�i�C Gb� 22 0 obj << >> Ӿ2�w /Filter /FlateDecode x�Mͱ�0�ᝧ��=ﮭ�*с���: !1֠��텢 �%��w;�ll�� � x��XYs�6~����I��`\���I�q�4��c��-Q2'e�J:����E���N�$��bw�LJ�Œ, #/Xo�0r��ˆԂ��ʅ&��,�� �ۑFu��J��L_=�V� ��!�%�Q޻���!9�"'�!���9�c':�$����E���B[fa=�9�DRir)� 6�2�1yGޡ�Q$����C�NE��Pe�5dڐ"�x�x$�`�@Y��[m�q��L]�hߗX;�F�"�~��ijsi1 l(v95`�����K�"��s��\�`[�2�af�f.S�{ 1����ų!GfɸIKz�T?J��=3�hf�\��:-X�BRt#��e� �D�+Ds�h�}�J;>��DM �Ղ�V�Q��������N���0�Й5�kj�����>����$�Z3�� /Type /XObject /Resources 87 0 R /Fm4 83 0 R There are various formulations of mean eld theory, but perhaps the best appreciated one is the Landau’s mean eld theory approach. /Contents 19 0 R /Parent 10 0 R endstream )�iM�}�,XjT\X������Dh�(��|ۻC3������2T�W��xݺ%׋�}h�q�_��؆������|�7�cN8e��T(F��00�>ǐ�LiM��cX����_�d�I�tVojV� OM� ������s*c�>a����� /Length 1079 Lecture notes copyright © 2017 David Tong unless Mean Field Theory for the Transverse Field Ising Model. x��XKo7��W�(��=�p�U����֖P=ⵒ6���!���Zq\���,������ ��H( ���LYɽ2L:�AZ���rt~K��R`�[���+�;�|n��z���5Wl��5z�_`R��1� �Y�]��-qv�&�T����H�y.m�]p���;��D1���`�ltN�^��O�)�mj.��:����G�.2�� endstream /Type /XObject A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. From Spins to Fields: PDF Introduction; The Ising Model; Landau Mean Field Theory, Universality, Critical Exponents; Landau-Ginzburg Theory, Domain Walls, The Lower Critical Dimension. >> endobj << Mean field theory for Fluids; Critical exponent of a fluid system; Mean field theory for magnetic systems; Mean field equation of state and its solution; Mean field critical exponents endobj Rönnow et al. 6 0 obj Mean Field m i = tanh( X j J ijm j); i = 1;:::;N (1) Note I The intractable task of computing marginals has been replaced by the problem of solving a set of nonlinear equations. /BBox [0 0 10.959 13.948] /Length 15 /Length 15 18 0 obj << The lecture notes come in around 130 pages and can be downloaded below. |�%�,HThۣ�ۖ������l%�/���s��X{���o������~IСa]0�OeQ“��d����m%y��6��8ϊ�ʳ�������Yb�|ݻ�ã�\�c!ѕc�-�=֗��3FpʍK����҃��8���. \ ���Qދ��/�?,t�y9f��SZ��~�bI�i��[�)ۮ28�!7��+�-���e�1ͩ�7��`�|@C�)�7��� 1. %���� /Type /XObject x���P(�� �� 2. For the Ising model, these can be related to the parameter Jby using the mean- eld approximation; this is discussed in section 7.3. /ProcSet [ /PDF /Text ] /Filter /FlateDecode /PTEX.FileName (/usr/local/texlive/2014/texmf-dist/tex/latex/beamer/art/beamericonarticle.pdf) endobj 3ۄĵb����4��>�Ɲ5c��`�d#�q���S6}L�{י11�>~�g=[?�V�1q7�Tfo޶��45V endobj )�� ��{#�����>���_'��׾�%Rs2�ᾠ�$\a�ɔ�5����\���?�w_dz^^\��*^��ǀW��5���(ކջV�߹��'-��E��K���u5!��y��ף1���ݪ�����v��buXվw�gq'0gq�?�bY��@V�i�^l6#��[��ϋ�8,֫��dd���eb�X���׷�j��%2z��hL��~4���\������,�u������y�&�{��. stream stream /Filter /FlateDecode >> 19 0 obj << >> /Filter /FlateDecode /Matrix [ 1 0 0 1 0 0] �+���գ���ޛisI�}:�y6�ܦ�f������)�t:��µ`iHV��`�a2^�d�8��z7�Wәe��ɘh���3�\;�m+��`G��ː����5`@r�)+�y��Oo�|t���ka��ƶ�u�(]�����>g���3+�5&�B*a�iFH��n.��?%H݋ Mean-Field Theory for Percolation Models of the Ising Type L. Chayes,1 A. Coniglio,2 J. Machta,3 and K. 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