Universality And Renormalization
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Author | : Ilia Binder |
Publisher | : American Mathematical Soc. |
Total Pages | : 414 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821842730 |
Download Universality and Renormalization Book in PDF, Epub and Kindle
This book covers a wide range of phenomena in the natural sciences dominated by notions of universality and renormalization. The contributions in this volume are equally broad in their approach to these phenomena, offering the mathematical as well as the perspective of the applied sciences. They explore renormalization theory in quantum field theory and statistical physics, and its connections to modern mathematics as well as physics on scales from the microscopic to the macroscopic. Information for our distributors: Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Author | : Michael E. Fisher |
Publisher | : |
Total Pages | : 278 |
Release | : 2000 |
Genre | : Renormalization (Physics) |
ISBN | : |
Download Scaling, Universality, and Renormalization Group Theory Book in PDF, Epub and Kindle
Author | : John Cardy |
Publisher | : Cambridge University Press |
Total Pages | : 264 |
Release | : 1996-04-26 |
Genre | : Science |
ISBN | : 9780521499590 |
Download Scaling and Renormalization in Statistical Physics Book in PDF, Epub and Kindle
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
Author | : Hidetoshi Nishimori |
Publisher | : Oxford University Press |
Total Pages | : 373 |
Release | : 2011 |
Genre | : Science |
ISBN | : 0199577226 |
Download Elements of Phase Transitions and Critical Phenomena Book in PDF, Epub and Kindle
As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.
Author | : Daniel J Amit |
Publisher | : World Scientific Publishing Company |
Total Pages | : 412 |
Release | : 1984-08-31 |
Genre | : |
ISBN | : 9813104147 |
Download Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition) Book in PDF, Epub and Kindle
This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.
Author | : Igor Herbut |
Publisher | : Cambridge University Press |
Total Pages | : 223 |
Release | : 2007-01-04 |
Genre | : Science |
ISBN | : 1139460129 |
Download A Modern Approach to Critical Phenomena Book in PDF, Epub and Kindle
Critical phenomena is one of the most exciting areas of modern physics. This 2007 book provides a thorough but economic introduction into the principles and techniques of the theory of critical phenomena and the renormalization group, from the perspective of modern condensed matter physics. Assuming basic knowledge of quantum and statistical mechanics, the book discusses phase transitions in magnets, superfluids, superconductors, and gauge field theories. Particular attention is given to topics such as gauge field fluctuations in superconductors, the Kosterlitz-Thouless transition, duality transformations, and quantum phase transitions - all of which are at the forefront of physics research. This book contains numerous problems of varying degrees of difficulty, with solutions. These problems provide readers with a wealth of material to test their understanding of the subject. It is ideal for graduate students and more experienced researchers in the fields of condensed matter physics, statistical physics, and many-body physics.
Author | : Vieri Mastropietro |
Publisher | : World Scientific |
Total Pages | : 303 |
Release | : 2008 |
Genre | : Science |
ISBN | : 9812792392 |
Download Non-perturbative Renormalization Book in PDF, Epub and Kindle
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providing a mathematical construction of models at low dimensions and discussing the removal of the ultraviolet and infrared cut-off, the verification of the axioms and the validity of Ward Identities with the relative anomalies. The second part is devoted to lattice 2D Statistical Physics, analyzing in particular the theory of universality in perturbed Ising models and the computation of the non-universal critical indices in Vertex or Ashkin-Teller models. Finally the third part is devoted to the analysis of complex quantum fluids showing Luttinger of Fermi liquid behavior, like the 1D or 2D Hubbard model.
Author | : Curtis T. McMullen |
Publisher | : Princeton University Press |
Total Pages | : 214 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400882559 |
Download Complex Dynamics and Renormalization (AM-135), Volume 135 Book in PDF, Epub and Kindle
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.
Author | : John C. Collins |
Publisher | : Cambridge University Press |
Total Pages | : 393 |
Release | : 2023-07-31 |
Genre | : Science |
ISBN | : 1009401769 |
Download Renormalization Book in PDF, Epub and Kindle
Author | : Ulrich Köbler |
Publisher | : Springer Science & Business Media |
Total Pages | : 402 |
Release | : 2010-04-29 |
Genre | : Technology & Engineering |
ISBN | : 3642024882 |
Download Renormalization Group Theory Book in PDF, Epub and Kindle
Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are called GSW bosons after Goldstone, Salam and Weinberg and in the case of superconductors the relevant field particles are called SC bosons. One can imagine these bosons as magnetic density waves or charge density waves, respectively. Crossover from atomistic exchange interactions to the excitations of the infinite solid occurs because the GSW bosons have generally lower excitation energies than the atomistic magnons. According to the principle of relevance the dynamics is governed by the excitations with the lowest energy. The non relevant atomistic interactions with higher energy are practically unimportant for the dynamics.