/Resources 87 0 R ���U�������2����ʷx8���J��4��U��-F�LS�x�5�l���q��D_�k�'��͘g:o1��͎�$��fv��z������4����⦅�ɮt�^×FS�f�3��љ֦T�Q�Ɂ��.T��J���W@��h�G->�]�K1۲�����kWa�s�nʰ �~h��� m,kbI$S��`�gR)�!c�����6� � stream }����s+b���&32�(�s�$���N:�*���?�҂����q�1�L�(�f���.ߦ��ohe��2���s�F{9w~�%T�[�agA�ɬ-���s��Bqg���׷F�te��Z�������袬�,aA`���8,1@j��z+%槭���+���L��kG����IU8��@��X�C+4���D�9%�l�V*[;]z�Yo�Q�� ,X�(���,߹�U�`f�c"��!�P7����me�-^��_����(����������lB�.�S������p6ޥ�d;N�7�ư�N��d?�"�D|cxgI�忽��={]v�Ti��a����ci���1Jr�B~��pD��A"�NC�#��"ȶ��n4��Ӿ���R؋�ĕ�WƔJ �A#zx����:\ ��}��ltrJ�Hs��d3|�HtI�]`������U=�N�J���^/�Ӎg�z7A�|��>;{ �螺f���F�R��b�p��|_�֛���R��l����q3�"�lj5�d�Y9||���S�n�'S��xwI�z�b]W�fU����|�H?�6�����^��uݬ�WѼ�C��&[o����o�Շ��Y� ��ɩ���:fč��7{k�w�h�׋�I� ���ގ?���Ň�M��[J�`$m�g��6�D^��|}���&}H�^�?MiM 36 0 obj endstream >> endobj 12 0 obj << /MediaBox [0 0 595.276 841.89] 0_8��X�" ��Z��E�����kn�!�ba!�"�D��7X2kVp�|N�%�fa�b ¬�@�#����q��hF���!����\)�Hc�E}�����R�_{��{��o 22 0 obj << The sign of cmust be positive, in order that the free energy be bounded from below. /Type /XObject stream 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�����>����$�Z3�� These lecture notes provide a detailed introduction to phase transitions and the /Length 448 /Type /Page /Filter /FlateDecode /Filter /FlateDecode Though mean eld theory often leads to answers which differ from their actual values, it has always been the rst approach taken by reseachers to predict the phase diagrams. endstream >> endobj /FormType 1 74 0 obj /Parent 10 0 R )�iM�}�,XjT\X������Dh�(��|ۻC3������2T�W��xݺ%׋�}h�q�_��؆������|�7�cN8e��T(F��00�>ǐ�LiM��cX����_�d�I�tVojV� OM� ������s*c�>a����� %���� 2. /Interpolate false << /Matrix [ 1 0 0 1 0 0] 1. 18 0 obj << << Consider a system of half integer Ising spins with the Hamiltonian H = -JEơi dj -T -roiz where ir = - (); =(:-), This model was originally proposed by de Gennes (69) and has recently been much studied as a model for "quantum phase transitions” in systems such as LiHoF4 (see e.g. /Matrix [ 1 0 0 1 0 0] >> << >> stream x��XKo7��W�(��Ǵh�$(jǺ�=,V+K�Vo���\r���v�$N@\9��f�0�f�:-`�nQˆМZ�7��dW������m�0�~2*�Gr�}��V�������nHG�!����pTsC �%e=ؒ����&�����K�ʖXʵcǍ3���!�i��w�5�"�+�i%i~�� O$0ؔ��?� ��9Kj��%$p��&+&|�;pff7���9����X����ҢHbH)I� ~ � �O���.����,�,D*ή� ��w����=�iE�)�/h{f�U��}0:Dƚd�&я�ʖ�m�$��2�͟�9=�ܮ�,����m-�8��Y�~�~�+�����������YC{�þa���$m�=�.�՚��G�c��nE��bN{p�ݦ���I-����a�*Kҵ#YH��H�%��@&! 83 0 obj endstream endobj /Length 1458 >>/ProcSet [ /PDF ] 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. /Resources 1 0 R /Resources 11 0 R >> endobj Lecture notes copyright © 2017 David Tong unless /Filter /FlateDecode stream >> stream Applying of correlation inequalities, i.e. /Filter /FlateDecode 17 0 obj << /Fm2 82 0 R << xڝTKn� �s Rönnow et al. /Length 447 x�mRMO�0���19��g�����X@%�T!&q����A��ہ����ϼ�捿6�/;���5=b\`QqT�S�P�=d?���*�Q���:8��D$��Eɲ�!��H��p��}���&��y�+�݆������`Z�~q��`�V�m��>�مx2Qĩ��)`-�XH)T0�9�����`�d���Om� �`����ϭ�Z����8���4;��q��s4�3B3�A����p�^,�c��R�� C[k��?�1e�t�%{�|��6� << /Subtype /Form /PTEX.PageNumber 1 Ising model and its applications; Other models and their ground states ; Universality in different models; Problems and Hints 4; References 4; Mean field theory. /Contents 19 0 R )�� ��{#�����>���_'��׾�%Rs2�ᾠ�$\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�&�{��. For the Ising model, these can be related to the parameter Jby using the mean- eld approximation; this is discussed in section 7.3. /MediaBox [0 0 595.276 841.89] stream /Type /XObject stream x���P(�� �� 112 0 obj /PTEX.FileName (/usr/local/texlive/2014/texmf-dist/tex/latex/beamer/art/beamericonarticle.pdf) endstream /Length 15 /Subtype /Form .����Ug]͢�]L��U�_���3J��B ��{�����]�j�g���'��k���oj��h' �$f܌wh��7[Ĥg6ŵ�1*�sL$J*;H�_k%���|�W� ����r�L�/���to�eG7��=���>��m����}����訣������4g����'�n\,�f�ޏM r����N���]�� /Length 863 Mean-Field Theory for Percolation Models of the Ising Type L. Chayes,1 A. Coniglio,2 J. Machta,3 and K. Shtengel4 Received February 9, 1998; final August 20, 1998 The q=2 random cluster model is studied in the context of two mean-field models: the Bethe lattice … /Subtype /Form endobj /Font << /F23 6 0 R /F27 16 0 R >> stream The lecture notes come in around 130 pages and can be downloaded below. [�C�)��H�2�H�3��G�$�l��w��~wTj>F�2�f$ /Length 15 endobj /FormType 1 82 0 obj << /Length 164 stream /Type /Page x���P(�� �� << /Contents 3 0 R Perimeter Institute Statistical Physics Lecture Notes part 7. endobj 13 0 obj << /Length 1132 (257) and references therein). Phase transitions: the song of fire and ice. }o�~o /�ܻ"�uY��0�g*��:���_�^�ؓ�k��� ���?l�� \ ���Qދ��/�?,t�y9f��SZ��~�bI�i��[�)ۮ28�!7��+�-���e�1ͩ�7��`�|@C�)�7��� /Type /XObject endstream >> >> endobj �8�������HS��e? 11 0 obj << Once the theoretical considerations for quantum criticality in the transverse field Ising model became known, the search began for a real material to display this QPT. endobj 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�� Unbinding of a vortex-anti-vortex pair in the Kosterlitz-Thouless transition, by Brian Skinner. 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� masters level) students. There are various formulations of mean eld theory, but perhaps the best appreciated one is the Landau’s mean eld theory approach. ��9O�b��'�u ��Í�)7!PE=+�s�Ya* |*���tlԇP �����B� �,�r��q添����B��,�E��`�5���4 �wc�W�E�4�\����U���[�iA{T/��X�6�2P�T�ҋ��p4��gf����h,Th� `��Bv\ �q�K��p\�Nu�\90W�EZڞ�2��8�(�FSW��P��^7B���9+A�� �n��G��]�5X�l#�G Al#�cR�B;.��Soˉ8��?���N�m7�jؑ1h��׫A��a��͡1��_���a����. f�f�7'Y��/'���6`� /Font << /F23 6 0 R >> /Resources 17 0 R /Fm3 84 0 R /BBox [0 0 10.959 13.948] >> attribution is given, no alterations are made, and no monetary profit is gained. 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 endstream %PDF-1.5 /BBox [ 0 0 19.925 14.944] 2 0 obj << 84 0 obj xڥ�M��0���>��;GZ��*H@��ڃi�f�$.I���{�|�EۊC)��;�x�]���'! /Type /Page Mean Field Theory for the Transverse Field Ising Model. Permission is granted to copy and distribute freely, so long as proper /Contents 13 0 R endstream otherwise credited. 6 0 obj /Filter /FlateDecode /Resources 86 0 R x�Mͱ�0�ᝧ��=ﮭ�*с���: !1֠��텢 �%��w;�ll�� � 19 0 obj << endobj My First Path Integral: PDF /Filter /FlateDecode /Matrix [ 1 0 0 1 0 0] /Filter /FlateDecode >> /BBox [ 0 0 2.491 3.487] The ground state was determined to be-36. Using natural path integral expansions, this quan-tum model reduces via a large deviation principle to a variational problem. A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. endstream 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. >> /ProcSet [ /PDF /Text ] /MediaBox [0 0 595.276 841.89]

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