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Author: Alicia J. Couto Galli
Publisher:
ISBN:
Category :
Languages : en
Pages : 150
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Book Description
Author: Alicia J. Couto Galli
Publisher:
ISBN:
Category :
Languages : en
Pages : 150
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Book Description
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 298
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Book Description
Author: Philippe Christe
Publisher: Springer Science & Business Media
ISBN: 3540475753
Category : Science
Languages : en
Pages : 260
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Book Description
The history of critical phenomena goes back to the year 1869 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 is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau's general theory of critical phenomena. In a dramatic development, Onsager's exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in the subsequent developments leading to the scaling theories of critical phenomena and the renormalization group. These developements have achieved a precise description of the close neighborhood of the critical point and results are often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is today emphasized.
Author: Claude Itzykson
Publisher: World Scientific
ISBN:
Category : Science
Languages : en
Pages : 0
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Book Description
This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions. Sample Chapter(s). Section 1: General Principles (4,851 KB). Contents: General Principles: Infinite Conformal Symmetry in Two-dimensional Quantum Field Theory (A A Belavin et al.); Conformal Invariance and Surface Critical Behaviour (J Cardy); Mathematical Background: Contravariant Form for Infinite-dimensional Lie Algebras and Superalgebras (V Kac); Verma Modules over the Virasoro Algebra (B Feigin & D Fuks); Unitary Representations of the Virasoro and Super-Virasoro Algebras (P Goddard et al.); Critical Models and Computation of Correlations: Conformal Algebra and Multipoint Correlation Functions in 2D Statistical Models (Vl Dotsenko & V Fateev); On the Identification of Finite Operator Algebras in Two-dimensional Conformally Invariant Field Theories (P Christe & R Flume); Finite Size Scaling: Conformal Invariance, the Central Charge and Universal Finite Size Amplitudes at Criticality (H BlAte et al.); Universal Term in the Free Energy at a Critical Point and the Conformal Anomaly (I Affleck); Exact Surface and Wedge Exponents for Polymers in Two Dimensions (B Duplantier & H Saleur); Modular Invariance: Modular Invariant Partition Functions in Two Dimensions (A Cappelli et al.); Modular Invariant Partition Functions for Parafermionic Field Theories (D Gepner & Z Qiu); Discrete Symmetries of Conformal Theories (J-B Zuber); Connections With Integrable Systems: Exact Exponents for Infinitely many New Multicritical Points (D Huse); Automorphic Properties of Local Height Probabilities for Integrable Solid-on-solid Models (E Date et al.); Models with c = 1: Correlation Functions on the Critical Lines of the Baxter and Ashkin-Teller Models (L Kadanoff & A Brown); Supersymmetric Critical Phenomena and the Two Dimensional Gaussian Model (D Friedan & S Shenker); Curiosities at c=1 (P Ginsparg); Coulomb Gas Picture: Lattice Derivation of Modular Invariant Partition Functions on the Torus (V Pasquier); Vicinity of the Critical Point: Integrals of Motion in Scaling 3-state Potts Model Field Theory (A Zamolodchikov); Correlation Functions and Higher Topology: The Conformal Field Theory of Orbifolds (L Dixon et al.); Conformal and Current Algebras on a General Riemann Surface (T Eguchi & H Ooguri); and other papers. Readership: Theoretical physicists in particle and statistical physics and mathematicians."
Author: Malte Henkel
Publisher: Springer Science & Business Media
ISBN: 3642279333
Category : Language Arts & Disciplines
Languages : en
Pages : 200
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Book Description
Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.
Author:
Publisher:
ISBN:
Category : Nuclear energy
Languages : en
Pages : 958
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Author: C Itzykson
Publisher: World Scientific
ISBN: 9814507598
Category :
Languages : en
Pages : 992
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Book Description
This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions.
Author: Clay Mathematics Institute. Summer School
Publisher: American Mathematical Soc.
ISBN: 0821868632
Category : Mathematics
Languages : en
Pages : 481
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Book Description
This volume is a collection of lecture notes for six of the ten courses given in Buzios, Brazil by prominent probabilists at the 2010 Clay Mathematics Institute Summer School, ``Probability and Statistical Physics in Two and More Dimensions'' and at the XIV Brazilian School of Probability. In the past ten to fifteen years, various areas of probability theory related to statistical physics, disordered systems and combinatorics have undergone intensive development. A number of these developments deal with two-dimensional random structures at their critical points, and provide new tools and ways of coping with at least some of the limitations of Conformal Field Theory that had been so successfully developed in the theoretical physics community to understand phase transitions of two-dimensional systems. Included in this selection are detailed accounts of all three foundational courses presented at the Clay school--Schramm-Loewner Evolution and other Conformally Invariant Objects, Noise Sensitivity and Percolation, Scaling Limits of Random Trees and Planar Maps--together with contributions on Fractal and Multifractal properties of SLE and Conformal Invariance of Lattice Models. Finally, the volume concludes with extended articles based on the courses on Random Polymers and Self-Avoiding Walks given at the Brazilian School of Probability during the final week of the school. Together, these notes provide a panoramic, state-of-the-art view of probability theory areas related to statistical physics, disordered systems and combinatorics. Like the lectures themselves, they are oriented towards advanced students and postdocs, but experts should also find much of interest.
Author: M Jimbo
Publisher: Elsevier
ISBN: 0323150357
Category : Science
Languages : en
Pages : 439
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Book Description
Advanced Studies in Pure Mathematics, 16: Conformal Field Theory and Solvable Lattice Models contains nine papers based on the symposium "Conformal field theory and solvable lattice models" held at RIMS, Kyoto, May 1986. These papers cover the following active areas in mathematical physics: conformal field theory, solvable lattice models, affine and Virasoro algebra, and KP equations. The volume begins with an analysis of 1 and 2 point correlation functions of the Gibbs measure of random matrices. This is followed by separate chapters on solvable solid-on-solid (SOS) models; lectures on conformal field theory; the construction of Fermion variables for the 3D Ising Model; and vertex operator construction of null fields (singular vertex operators) based on the oscillator representation of conformal and superconformal algebras with central charge extention. Subsequent chapters deal with Hecke algebra representations of braid groups and classical Yang-Baxter equations; the relationship between the conformal field theories and the soliton equations (KdV, MKdV and Sine-Gordon, etc.) at both quantum and classical levels; and a supersymmetric extension of the Kadomtsev-Petviashvili hierarchy.
Author: Malte Henkel
Publisher: Springer Science & Business Media
ISBN: 9783540653219
Category : Mathematics
Languages : en
Pages : 440
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Book Description
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.
