1 edition of Conformal Invariance and Critical Phenomena found in the catalog.
This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are also reviewed.
|Statement||by Malte Henkel|
|Series||Texts and Monographs in Physics, Texts and Monographs in Physics|
|The Physical Object|
|Format||[electronic resource] /|
|Pagination||1 online resource (xvii, 417 p.)|
|Number of Pages||417|
|ISBN 10||3642084664, 3662039370|
|ISBN 10||9783642084669, 9783662039373|
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified.. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum. Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models. E. Martinec and S. Shenker, Conformal invariance, supersymmetry and string theory Nucl. Phys. B Crossref Google Scholar  Quantum field theory and critical phenomena 2 nd ed., Oxford Univ. Press () Google Scholar.
Conformal Invariance of Ising Model Correlations Hongler, Clément We review recent results with D. Chelkak and K. Izyurov, where we rigorously prove existence and conformal invariance of scaling limits of magnetization and multi-point spin correlations in the critical Ising model on an arbitrary simply connected planar domain. Conformal invariance enables a thorough classification of universality classes of critical phenomena in 2D. Is there conformal invariance in 2D turbulence, a paradigmatic example of a .
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Conformal Invariance and Critical Phenomena (Theoretical and Mathematical Physics) th Edition by Malte Henkel (Author) ISBN Cited by: The history of critical phenomena goes back to the year when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure.
In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered.
This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators.
Introduction to Conformal Invariance and Its Applications to Conformal Invariance and Critical Phenomena book Phenomena (Lecture Notes in Physics Monographs) (Lecture Notes in Physics Monographs (16)) Softcover reprint of Reviews: 1.
Critical Phenomena: a Reminder -- 2. Conformal Invariance -- 3. Finite-Size Scaling -- 4. Representation Theory of the Virasoro Algebra -- 5. Correlators, Null Vectors and Operator Algebra -- 6. Ising Model Correlators -- 7. Coulomb Gas Realization -- 8.
The Hamiltonian Limit and Universality -- 9. Numerical Techniques -- Conformal. Conformal Invariance and Critical Phenomena With 65 Figures and 63 Tables Springer. Contents 1. Critical Phenomena: a Reminder 1 Phase Diagrams and Critical Exponents 1 Scale Invariance and Scaling Relations 6 Some Simple Spin Systems 12 Ising Model Conformal invariance constrains the form of correlation functions near a free surface.
In two dimensions, for a wide class of models, it completely determines the correlation functions at the critical point, and yields the exact values of the surface critical exponents. They are related to the bulk exponents in a non-trivial way.
Introduction to Conformal Invariance and Its Applications to Critical Phenomena的话题 (全部 条) 什么是话题 无论是一部作品、一个人，还是一件事，都往往可以衍生出许多不同的话题。.
From Random Walks to Critical Phenomena and Conformal Field Theory Benjamin Hsu May 4, Abstract In class, we approached critical phenomena from the view point of correlation func- a very speci c and physically clear picture of what it means to be conformally invariant .
C Itzykson and J M Drouffe, Statistical Field Theory,vols. Cambridge ) M Henkel, Conformal Invariance and Critical Phenomena(Springer, ) - more from the point of view of critical behaviour C Itzykson, H Saleur and J-B Zuber, Conformal Invariance and Applications to Statistical Mechanics,(World Scientific, ).
In the last chapter, conformal invariance was used to constrain the multipoint correlation functions of isotropic critical two-dimensional systems. Before following the field-theoretic developments. The use of the conformal symmetry is well appreciated in the literature, but the fact that all the scale invariant phenomena in dimension enjoy the conformal property relies on the deep structure of the renormalization group.
The outstanding question is whether this feature is specific to dimension or it holds in higher dimensions, too.
Critical phenomena arise in a wide variety of physical systems. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical.
Zamolodchikov A.A., Zamolodchikov Al.B. Conformal field theory and critical phenomena in 2d systems (part of a book, p) p. English djvu, KB KB/p. dpi OCR | File | Henkel M. Conformal invariance and critical phenomena Springer, X p. English djvu, KB KB/p.
dpi OCR. 1. Introduction. The theory of conformal invariance has provided considerable fundamental insight in critical phenomena by predicting spectra of critical exponents in two-dimensional models.Other interesting theoretical results follow from conformal mappings of correlation functions between models defined in different geometries.
Abstract: This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their application to the Ising, Potts, Ashkin-Teller and XY models, tricritical behaviour, the Yang-Lee singularity and the XXZ chain are presented.
Conformal Invariance and Critical Phenomena de Malte Henkel - English books - commander la livre de la catégorie Physique et astronomie sans frais de port et bon marché - Ex Libris boutique en Edition: Conformal Invariance and Critical Phenomena的话题 (全部 条) 什么是话题 无论是一部作品、一个人，还是一件事，都往往可以衍生出许多不同的话题。.
BOOK EXCERPT: Conformal Invariance and String Theory is an account of the series of lectures held in Summer School regarding Conformal Invariance and String Theory in September The purpose of the lectures is to present the important problems and results in these two areas of theoretical physics.
The text is divided into two major parts. conformal invariance. We observe that the statistics of vorticity clusters are remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a key step in the uniﬁcation of 2D physics within the framework of conformal symmetry.
History. The idea of scale transformations and scale invariance is old in physics: Scaling arguments were commonplace for the Pythagorean school, Euclid, and up to Galileo. They became popular again at the end of the 19th century, perhaps the first example being the idea of enhanced viscosity of Osborne Reynolds, as a way to explain turbulence.
The renormalization group was initially devised.A detailed consideration of ideal (random walk-type) chains near surfaces serves as a first orientation.
Much of the materials have not appeared previously in book form. This text is the first to give an introduction simultaneously to the renormalization group, short distance expansions and conformal invariance in critical systems with a surface.Questions • Is the connection with 2D classical systems peculiar to the QDM?
Conformal invariance in 2D? Central charge? • Is this quantum phase transition generic?, i.e. is it robust to local short range perturbations of the QDM? • Why this is not a ﬁrst order transition (as naively expected)?
• QDM models are known to have columnar, plaquette and “staggered" phases.