Many researchers now find themselves working away from their institutions and, thus, may have trouble accessing the Physical Review journals. We continue the considerations of the first paper in this series by studying the time dependence of the spin-correlation functions in response to a step-function change in the external magnetic field. Physical Review A™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. So I looked for the book and I finally found the answer (cap. While for the Ising and Potts model it is easy to find information, it's quite difficult for me to understand when and where the XY model (or the plane rotator model) was first presented. I think I found the answer. Freely browse and use OCW materials at your own pace. in the XY model, known as the topological defect. x�}ɮ�F잯ps��gU�hkOI��)�����a�4��%G3�{�ח�6���C��N�o_��!.6� There's no signup, and no start or end dates. ), Learn more at Get Started with MIT OpenCourseWare, MIT OpenCourseWare makes the materials used in the teaching of almost all of MIT's subjects available on the Web, free of charge. Why is it easier to carry a person while spinning than not spinning? The classical XY model (sometimes also called classical rotor (rotator) model or O(2) model) is a lattice model of statistical mechanics. I hope the (hi)story is concluded! Publication: Physical Review A. Pub Date: … 3 0 obj << /Filter /FlateDecode Physics Each lattice site hosts a magnetic dipole, illustrated by the little needles below. … Dirk Brockmann. » Mentor added his name as the author and changed the series of authors into alphabetical order, effectively putting my name at the last. Home ���7��MY�U�o�*���<6���wG}�f���"��ߏ�o��NUa�L�V;[�}�j�nt^{���8�z�&�Qw�v��d�%���L�jlFĜm'����D��{\�I�)��qX�"(��.��,xw���e�8�,KDX��I����#j����g2��iZ�hc�mR�� 1],4 P4 �Q���c�p�S�ڌY�f3P�X�J嬷PT�4F��_�0��6)38�w�1d ����3��I�i�����]�^��� ��G����iy���V���tGS��H�o�2 �]�A91��\ܑ���Uh����3xk#�!eږ�Ƹz�OL�����h�j�׻{x�>nPy������E�U�H��BB���(����^���� ���m� Statistical Mechanics II: Statistical Physics of Fields Use MathJax to format equations. Is there a name for applying estimation at a lower level of aggregation, and is it necessarily problematic? It only takes a minute to sign up. All rights reserved. The same Lieb and Mattis @Yvan Velenik reported in his answer. Kac, M. “The Work of T.H. But thanks to it, I found an interesting historical paper written by Kac himself, where he tells the story of his model. Did Maxwell discover the distribution of velocities in a gas during an exam set by Stokes? Can you have a Clarketech artifact that you can replicate but cannot comprehend? We find that these correlation functions exhibit nonergodic behavior. History of Science and Mathematics Stack Exchange is a question and answer site for people interested in the history and origins of science and mathematics. I would like to find out more about the history of the XY model. With more than 2,400 courses available, OCW is delivering on the promise of open sharing of knowledge. Made for sharing. The APS Physics logo and Physics logo are trademarks of the American Physical Society. Quick link too easy to remove after installation, is this a problem? © Dirk Brockmann, 2020 Complexity Explorables. Part IV Quantum Statistical Mechanics 22 Quantum Ensembles 247 22.1 Basic Quantum Mechanics 248 22.2 Energy Eigenstates 248 22.3 Many-Body Systems 251 22.4 Two Types of Probability 252 22.5 The Density Matrix 254 22.6 The Uniqueness of the Ensemble 255 22.7 The Quantum Microcanonical Ensemble 256 23 Quantum Canonical Ensemble 258 It can be used to describe such diverse phenomena as magnets; liquid/gas coexistence; alloys of two metals; and many others, even outside of physics. The KT transition is quite famous (1972), but even in the original paper by Kosterlitz and Thouless there's nothing about history. Information about registration may be found here. Explore phase transitions through percolation! The $$XY$$-model is actually quite simple. MathJax reference. The article is: But I wasn't done. We continue the considerations of the first paper in this series by studying the time dependence of the spin-correlation functions in response to a step-function change in the external magnetic field. doi:10.1103/PhysRevLett.20.1507. In this case, the O(N) model was introduced later, I suppose. Thanks for contributing an answer to History of Science and Mathematics Stack Exchange! A 2, 1075 (1970) - Statistical Mechanics of the $\mathrm{XY}$ Model. Press Play and see what happens. Dipole $$n$$ then slowly aligns its orientation towards the average orientation of its neighbors. Agreement. Use, Smithsonian The final project counts for 25% of the course grade. Through this difficult time APS and the Physical Review editorial office are fully equipped and actively working to support researchers by continuing to carry out all editorial and peer-review functions and publish research in the journals as well as minimizing disruption to journal access. Is this a correct rendering of some fourteenth-century Italian writing in modern orthography? Where is this Utah triangle monolith located? Stanley, H. E. “Exact Solution for a Linear Chain of I. doi:10.1063/1.3051173. >> A Closer Look at the Frustrated Ising Model on a Hierarchical Lattice and Possible Phase Diagram Modifications; Vortex-Magnetic Field Duality in the Classical XY Model; Theoretical Models for One and Two Component Lipid Membranes; Vanishing gaps in random transverse Ising model: Difficulty and new strategy for the Quantum Adiabatic Algorithm �1L9ʡ�ADN1/��U>2��|�;a��gw�韼� &�&���K�E�z��^�݁�4�Z{��1�l�Z����� �J3(8+R�7��3B3�1�W�p�� As far as I know, this model (well, the quantum version of it) was introduced in the following paper: The paper can be found here. To address this, we have been improving access via several different mechanisms. The statistical mechanics of this generalised XY model is analysed mainly by considering the low-temperature behaviors. History of XY model - Plane Rotator model, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, “Question closed” notifications experiment results and graduation. Design a web site that can be used to teach a topic related to Collective Behaviors to non-specialists.