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Author: Ilia Binder
Publisher: American Mathematical Soc.
ISBN: 0821842730
Category : Mathematics
Languages : en
Pages : 414
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Book Description
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: Ilia Binder
Publisher: American Mathematical Soc.
ISBN: 0821842730
Category : Mathematics
Languages : en
Pages : 414
Get Book Here
Book Description
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:
ISBN:
Category : Renormalization (Physics)
Languages : en
Pages : 278
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Book Description
Author: John Cardy
Publisher: Cambridge University Press
ISBN: 9780521499590
Category : Science
Languages : en
Pages : 264
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Book Description
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: Daniel J Amit
Publisher: World Scientific Publishing Company
ISBN: 9813104147
Category :
Languages : en
Pages : 412
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Book Description
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
ISBN: 1139460129
Category : Science
Languages : en
Pages : 223
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Book Description
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: Hidetoshi Nishimori
Publisher: Oxford University Press
ISBN: 0199577226
Category : Science
Languages : en
Pages : 373
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Book Description
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: Curtis T. McMullen
Publisher: Princeton University Press
ISBN: 9780691029818
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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: Vieri Mastropietro
Publisher: World Scientific
ISBN: 9812792392
Category : Science
Languages : en
Pages : 303
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Book Description
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: John C. Collins
Publisher: Cambridge University Press
ISBN: 1009401769
Category : Science
Languages : en
Pages : 393
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Book Description
Author: Jurgen M. Honig
Publisher: Elsevier
ISBN: 0128048360
Category : Science
Languages : en
Pages : 256
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Book Description
A Primer to the Theory of Critical Phenomena provides scientists in academia and industry, as well as graduate students in physics, chemistry, and geochemistry with the scientific fundamentals of critical phenomena and phase transitions. The book helps readers broaden their understanding of a field that has developed tremendously over the last forty years. The book also makes a great resource for graduate level instructors at universities. - Provides a thorough and accessible treatment of the fundamentals of critical phenomena - Offers an in-depth exposition on renormalization and field theory techniques - Includes experimental observations of critical effects - Includes live examples illustrating the applications of the theoretical material
