Early Work on Defect Driven Phase Transitions
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Notes on Statistical Field Theory
Lecture Notes on Statistical Field Theory Kevin Zhou [email protected] These notes cover statistical field theory and the renormalization group. The primary sources were: • Kardar, Statistical Physics of Fields. A concise and logically tight presentation of the subject, with good problems. Possibly a bit too terse unless paired with the 8.334 video lectures. • David Tong's Statistical Field Theory lecture notes. A readable, easygoing introduction covering the core material of Kardar's book, written to seamlessly pair with a standard course in quantum field theory. • Goldenfeld, Lectures on Phase Transitions and the Renormalization Group. Covers similar material to Kardar's book with a conversational tone, focusing on the conceptual basis for phase transitions and motivation for the renormalization group. The notes are structured around the MIT course based on Kardar's textbook, and were revised to include material from Part III Statistical Field Theory as lectured in 2017. Sections containing this additional material are marked with stars. The most recent version is here; please report any errors found to [email protected]. 2 Contents Contents 1 Introduction 3 1.1 Phonons...........................................3 1.2 Phase Transitions......................................6 1.3 Critical Behavior......................................8 2 Landau Theory 12 2.1 Landau{Ginzburg Hamiltonian.............................. 12 2.2 Mean Field Theory..................................... 13 2.3 Symmetry Breaking.................................... 16 3 Fluctuations 19 3.1 Scattering and Fluctuations................................ 19 3.2 Position Space Fluctuations................................ 20 3.3 Saddle Point Fluctuations................................. 23 3.4 ∗ Path Integral Methods.................................. 24 4 The Scaling Hypothesis 29 4.1 The Homogeneity Assumption............................... 29 4.2 Correlation Lengths.................................... 30 4.3 Renormalization Group (Conceptual).......................... -
Solid State Physics 2 Lecture 4: Magnetism in Charge Insulators
Physics 7450: Solid State Physics 2 Lecture 4: Magnetism in charge insulators Leo Radzihovsky (Dated: 19 February, 2015) Abstract In these lectures, we will study magnetism in insulators. After a warm up with paramagnetism of independent spins, we will discuss the spin exchange interactions in solids, arising from the combination of Coulomb repulsion and Pauli exclusion, and leads to the Heisenberg model of magnetism. Focussing on the simplest ferromagnetic and antiferromagnetic states, we will analyze thermodynamics and correlations of low-energy excitations around these states using Holstein- Primakoff and Schwinger bosons descriptions. We will use Jordan-Wigner transformation to solve a one-dimensional spin-1/2 chain. We will discuss coherent-spin states path-integral formulation of magnetism emphasizing, the role of Berry’s phase and will analyze phase transitions using Landau’s mean-field theory of FM and AFM phases. 1 I. INTRODUCTION A. Outline • Paramagnetism • Spin exchange vs dipolar interaction • Heisenberg model and crystalline anisotropies • Hostein-Primakoff and Schwinger bosons • Jordan-Wigner transformation and XXZ chain • Coherent-spin states and Berry phases • Mean-field and Landau theory of FM and AFM states B. Background In these notes we will explore some of aspects of magnetism in charge insulators. Mag- netism is a formation and response of magnetic moments to external magnetic field H and their interaction. In general there are two sources of magnetic moment and associated mag- netization density M. One is quite intuitive, due to orbital charge current j in the material 1 Z M = r × j, 2 r much like current wire loop produces magnetic field. -
Melting of Two-Dimensional Tunable-Diameter Colloidal Crystals
PHYSICAL REVIEW E 77, 041406 ͑2008͒ Melting of two-dimensional tunable-diameter colloidal crystals Y. Han,* N. Y. Ha,† A. M. Alsayed, and A. G. Yodh Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6396, USA ͑Received 12 February 2007; revised manuscript received 24 November 2007; published 18 April 2008͒ Melting of two-dimensional colloidal crystals is studied by video microscopy. The samples were composed of microgel spheres whose diameters could be temperature tuned, and whose pair potentials were measured to be short ranged and repulsive. We observed two-step melting from the crystal to a hexatic phase and from the hexatic to the liquid phase as a function of the temperature-tunable volume fraction. The translational and orientational susceptibilities enabled us to definitively determine the phase transition points, avoiding ambigu- ities inherent in other analyses and resolving a “dislocation precursor stage” in the solid phase that some of the traditional analyses may incorrectly associate with the hexatic phase. A prefreezing stage of the liquid with ordered patches was also found. DOI: 10.1103/PhysRevE.77.041406 PACS number͑s͒: 82.70.Ϫy, 64.60.Cn, 64.70.DϪ I. INTRODUCTION to follow the spatiotemporal evolution of the same sample area through the entire sequence of transitions. This feature ͑ ͒ Two-dimensional 2D melting is a classic problem in is attractive and was not realized in previous colloidal melt- ͓ ͔ condensed matter physics 1 , and, over the years, theories ing experiments which employed samples composed of attempting to understand 2D melting have emphasized topo- charged spheres in the wedge geometry with density gradi- ͓ ͔ ͓ ͔ logical defects 2–5 , geometrical defects 6 , and grain ents ͓11͔, nor in experiments that employed samples com- ͓ ͔ boundaries 7 . -
Trends in Mathematical Crystallisation May 2016 Organiser: Stefan Adams, Markus Heydenreich, Frank Den Hollander, Sabine Jansen
Trends in mathematical crystallisation May 2016 Organiser: Stefan Adams, Markus Heydenreich, Frank den Hollander, Sabine Jansen Description and aim: The workshop concentrates on the mathematical theory of crystallisation. More precisely, we focus on five topics that are closely connected with crystallisation, and approach these topics from different mathematical angles. These five topics are: (1) Spatial symmetry breaking at positive temperature (2) Crystallisation and surface effects at zero temperature (3) Continuum particle systems (Gibbs point fields, metastability, and Percolation) (4) Elasticity (variational analysis & gradient fields and quasi-crystals and liquid crystals (5) Differential/integral geometry We expect participants from analysis, statistical physics and probability. Our primary goal is to discuss the different approaches towards crystallisation in these disciplines. Vision: Crystallisation is the (natural or artificial) process of formation of solid crystals precipitating from a solution, melt or more rarely deposited directly from a gas. Crystallisation is also a chemical solid-liquid separation technique, in which mass transfer of a solute from the liquid solution to a pure solid crystalline phase occurs. In chemical engineering crystallisation occurs in a crystalliser. Crystallisation is therefore an aspect of precipitation, obtained through a variation of the solubility conditions of the solute in the solvent, as compared to precipitation due to chemical reaction. Crystallisation poses major challenges for mathematicians - it is one of the challenging open interdisciplinary problems involving analysts, probabilists, applied mathematicians, physicists and material scientists. There are many open questions, among which are the following. Most of these have been discussed at the workshop 'Facets of mathematical crystallization' - Lorentz Center Leiden, September 2014. A key challenge of the workshop is to address and clarify their potential further. -
Asia Pacific Physics Newsletter
Asia Pacific Physics Newsletter March 2016 Volume 5 • Number 1 worldscinet.com/appn Takaaki Kajita 2015 Physics Nobel Laureate published by Institute of Advanced Studies, Nanyang Technological University (IAS@NTU) and South East Asia Theoretical Physics Association (SEATPA) South East Asia Theoretical Physics Association Asia Pacific Physics Newsletter March 2016 • Volume 5 • Number 1 A publication of the IAS@NTU Singapore and SEATPA Asia Pacific Physics Newsletter publishes articles reporting frontier discoveries in EDITORIAL physics, research highlights, and news to facilitate interaction, collaboration and 3 cooperation among physicists in Asia Pacific physics community. PEOPLE Editor-in-Chief 4 “Observing the Distant Supernova” — Interview with Kok Khoo Phua Nobel Laureate Prof Brian Schmidt Associate Editor-in-Chief “Discovering the W and Z Bosons” — Interview with Swee Cheng Lim Nobel Laureate Prof Carlo Rubbia SEATPA Committee Christopher C Bernido Phil Chan Leong Chuan Kwek Choy Heng Lai Swee Cheng Lim Ren Bao Liu Hwee Boon Low Anh Ký Nguyên Choo Hiap Oh OPINION AND COMMENTARY Kok Khoo Phua 10 China’s Great Scientific Leap Forward: Completion of a Roh Suan Tung Preecha Yupapin planned ‘Great Collider’ would transform particle physics Hishamuddin Zainuddin Freddy Zen Editorial Team NEWS Sen Mu 12 CityU’s Institute for Advanced Study will Champion Bold New Han Sun Chi Xiong Research Initiatives Case made for 'Ninth Planet' Graphic Designers Chuan Ming Loo Erin Ong Cover Photo: "Takaaki Kajita 5171- 2015" by Bengt Nyman - Own work. -
Valery Pokrovsky Landau and Theory of Phase Transitions
Landau and Theory of Phase Transitions Valery Pokrovsky Dept. of Physics, Texas A&M University and Landau Institute for Theoretical Physics Landau Centenary, APS March Meeting, March 18, 2009. Landau phenomenon Scirus Fermi liquids – 45,000 2008 Phase transitions -- 30,000 Landau levels -- 75,500 Landau-Lifshitz Equation -- 23,000 5 Nobel prizes based on Landau works: K. Wilson; P.-G. De Gennes; A.A. Abrikosov, V.L. Ginzburg, A. Legget; K. von Klitzing; D.Tsui, H. Störmer, R.B. Loughlin. Longevity of the LL Course 1940-20.. Landau Centenary, APS March Meeting, March 18, 2009. Extremely general and simple notions: Density matrix Spontaneous symmetry breaking Fermi liquid Quasiparticles Simple and effective formalism Phase transitions Landau levels Neutron stars Unique view of entire physics Landau Centenary, APS March Meeting, March 18, 2009. Landau theory of phase transitions: History Predecessors Curie-Weiss theory of self-consistent field in ferromagnets Ehrenfest theory of higher order transitions Landau: Contribution to theory of specific heat anomaly Phys. Zs. Sowjet., 8, 113 (1935) 23 - degree of order Φ=Φ0 +abξ +ξξ + c ξ aTT=−α ( c ) Landau Centenary, APS March Meeting, March 18, 2009. 3 articles published in 1937 in ZhETF and Phys. Zs. Sowjet. Theory of phase transitions I Concept of spontaneous symmetry violation. Ordered phase is characterized by some irreducibleOnly one IR representation appears near oftransition the initial point symmetry group. 24 ⎛⎞TT− c η 22= c Φ=abaηη +; = α ⇒∝η TT − δρϕ= c ∑ i ⎜⎟ c ∑ ni ni i ⎝⎠Tc ni, Specific heat has a finite jump at transition Theory of phase transitions II 1. -
Bond-Orientational Order and Frank's Constant in Two-Dimensional
IOP Journal of Physics: Condensed Matter Journal of Physics: Condensed Matter J. Phys.: Condens. Matter J. Phys.: Condens. Matter 30 (2018) 104003 (6pp) https://doi.org/10.1088/1361-648X/aaab31 30 Bond-orientational order and Frank’s 2018 constant in two-dimensional colloidal © 2018 IOP Publishing Ltd hard spheres JCOMEL Alice L Thorneywork1,2, Joshua L Abbott1, Dirk G A L Aarts1, Peter Keim3 and Roel P A Dullens1 104003 1 Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ, United Kingdom A L Thorneywork et al 2 Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom 3 Department of Physics, University of Konstanz, Konstanz 78464, Germany Bond-orientational order and Frank s constant in two-dimensional colloidal hard spheres ’ E-mail: [email protected] Printed in the UK Received 26 October 2017, revised 12 January 2018 Accepted for publication 29 January 2018 Published 15 February 2018 CM Abstract Recently, the full phase behaviour of 2D colloidal hard spheres was experimentally 10.1088/1361-648X/aaab31 established, and found to involve a first order liquid to hexatic transition and a continuous hexatic to crystal transition (Thorneywork et al 2017 Phys. Rev. Lett. 118 158001). Here, we expand upon this work by considering the behaviour of the bond-orientational correlation Paper time and Frank’s constant in the region of these phase transitions. We also consider the excess entropy, as calculated from the radial distribution functions, for a wide range of area fractions covering the liquid, hexatic and crystal phases. -
History of Physics Newsletter Volume VII, No. 3, Aug. 1998 Forum Chair
History of Physics Newsletter Volume VII, No. 3, Aug. 1998 Forum Chair From the Editor Forum News APS & AIP News Book Review Reports Forum Chair Urges APS Centennial Participation The American Physical Society celebrates its 100th anniversary in Atlanta, Georgia, at an expanded six-day meeting from March 20-26, 1999, which will be jointly sponsored by the American Association of Physics Teachers. This will be the largest meeting of physicists ever held, and the APS Forum on the History of Physics will play a central role in making it a truly memorable event. The 20th century has been the Century of Physics. The startling discoveries of X-rays, radioactivity, and the electron at the end of the 19th century opened up vast new territories for exploration and analysis. Quantum theory and relativity theory, whose consequences are far from exhausted today, formed the bedrock for subsequent developments in atomic and molecular physics, nuclear and particle physics, solid state physics, and all other domains of physics, which shaped the world in which we live in times of both peace and war. A large historical wall chart exhibiting these developments, to which members of the Forum contributed their expertise, will be on display in Atlanta. Also on display will be the well-known Einstein exhibit prepared some years ago by the American Institute of Physics Center for History of Physics. Two program sessions arranged by the Forum at the Atlanta Centennial Meeting also will explore these historic 20th-century developments. The first, chaired by Ruth H. Howes (Ball State University), will consist of the following speakers and topics: John D. -
Unit VI Superconductivity JIT Nashik Contents
Unit VI Superconductivity JIT Nashik Contents 1 Superconductivity 1 1.1 Classification ............................................. 1 1.2 Elementary properties of superconductors ............................... 2 1.2.1 Zero electrical DC resistance ................................. 2 1.2.2 Superconducting phase transition ............................... 3 1.2.3 Meissner effect ........................................ 3 1.2.4 London moment ....................................... 4 1.3 History of superconductivity ...................................... 4 1.3.1 London theory ........................................ 5 1.3.2 Conventional theories (1950s) ................................ 5 1.3.3 Further history ........................................ 5 1.4 High-temperature superconductivity .................................. 6 1.5 Applications .............................................. 6 1.6 Nobel Prizes for superconductivity .................................. 7 1.7 See also ................................................ 7 1.8 References ............................................... 8 1.9 Further reading ............................................ 10 1.10 External links ............................................. 10 2 Meissner effect 11 2.1 Explanation .............................................. 11 2.2 Perfect diamagnetism ......................................... 12 2.3 Consequences ............................................. 12 2.4 Paradigm for the Higgs mechanism .................................. 12 2.5 See also ............................................... -
Cornell Chemistry
CORNELL CHEMISTRY Chairman's Column Cornell's commitment to high-quality education in chemistry stands rooted in history: two of A. D. White's first four professorial appointments to the University faculty were chemists! Today, in the face of ever-rising costs and expectations, we, as a department, remain dedicated to that tradition. We must provide state-of-the-art training in chemistry for those of our majors who will pursue postgraduate education and careers in the physical or biological sciences, while also furnishing a realistic, comprehensive introduction to our discipline to the overwhelming majority of students (>90%) for whom undergraduate courses will be their only exposure to the concepts of modern chemical science. Striking a balance between these demands provides an ongoing challenge, as does the ceaseless search for the intellectual and financial resources required to maintain our tradition of excellence. THE NEWSLETTER Chemistry's role as "a science ministrant of sciences" (to quote the inscription above the main entrance of Baker Lab) imposes some unique demands upon us. Fortunately it also OF THE provides some unique, compensatory advantages! The vital breadth of the discipline is DEPARTMENT OF well illustrated by the scope of the research interests of our faculty, which this coming CHEMISTRY year will be joined by three new members. Coming to Cornell as Assistant Professors are Tadhg Begley, a bioorganic chemist who is concerned with enzymatic mechanisms AND THE SOCIETY OF and biomimetic processes, and Atsuo Kuki, a physical chemist who works on the role of CORNELL CHEMISTS solvent structure in fundamental phenomena such as electron transfer. -
BERG-DISSERTATION-2014.Pdf
Copyright by Morgann Elizabeth Berg 2014 The Dissertation Committee for Morgann Elizabeth Berg certifies that this is the approved version of the following dissertation: Magnetic Force Microscopy Studies of Magnetic Domain Structure in LaCoO3 and UMn2Ge2 Committee: Alejandro L. de Lozanne, Supervisor John T. Markert Maxim Tsoi Zhen Yao Jianshi Zhou Magnetic Force Microscopy Studies of Magnetic Domain Structure in LaCoO3 and UMn2Ge2 by Morgann Elizabeth Berg, B. S. Phy. Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy The University of Texas at Austin December, 2014 Dedication This dissertation is dedicated to my parents and to my families- the one I was blessed with, the ones I chose and the ones who chose me. But most especially this dissertation is dedicated to my son Devin. Of all the support I have received from family and friends this dissertation probably asked the most from him. He is the light that will light me up from within always. Acknowledgements I would like to thank my advisor Alex for so many things, but especially for his patience which I think I tested often. I thank him for welcoming me into his group and being a constant presence along my (sometimes meandering) path through doctoral research. There is a great deal about his methodology to admire and his example will always be something I look to. It feels like the amazing people I have worked with are too long to list, but I will do my best. -
Magnetic Behavior of Bulk and Nanostructured Mnxtas2
University of Northern Iowa UNI ScholarWorks Honors Program Theses Honors Program 2017 Magnetic behavior of bulk and nanostructured MnxTaS2 Lucas Paul Beving University of Northern Iowa Let us know how access to this document benefits ouy Copyright ©2017 - Lucas Paul Beving Follow this and additional works at: https://scholarworks.uni.edu/hpt Part of the Atomic, Molecular and Optical Physics Commons, and the Materials Science and Engineering Commons Recommended Citation Beving, Lucas Paul, "Magnetic behavior of bulk and nanostructured MnxTaS2" (2017). Honors Program Theses. 274. https://scholarworks.uni.edu/hpt/274 This Open Access Honors Program Thesis is brought to you for free and open access by the Honors Program at UNI ScholarWorks. It has been accepted for inclusion in Honors Program Theses by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. MAGNETIC BEHAVIOR OF BULK AND NANOSTRUCTURED MnxTaS2 A Thesis Submitted in Partial Fulfillment of the Requirements for the Designation University Honors Lucas Paul Beving University of Northern Iowa May 2017 This Study by: Entitled: has been approved as meeting the thesis requirement for the Designation University Honors _________ _______________________________________________ Date Dr. Paul Shand, Honors Thesis Advisor, Physics Department _________ _______________________________________________ Date Dr. Jessica Moon, Director, University Honors Program MAGNETIC BEHAVIOR OF BULK AND 1 Introduction At its base, material science research aims to categorize specific materials by their various attributes, such as structure, integrity, electronic properties, magnetic properties, and others. By categorizing materials in this way, it becomes easier to generalize the application of a specific material to those within a broader category.