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Renormalization group and scaling

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Mean-field theory is usually taken as a first step toward understanding critical phenomena, providing an overview that reveals qualitative behaviour of physical quantities. However, it is necessary ... More


Elements of Phase Transitions and Critical Phenomena

Hidetoshi Nishimori and Gerardo Ortiz

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into ... More


Implementation of the renormalization group

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Actual computations of fixed points and eigenvalues usually involve approximations, often crude ones, except for a very limited number of simple cases such as the one-dimensional Ising model of the ... More


Introduction to Renormalization Theory. Renormalization Group Equations

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the essential steps of the proof of the renormalizability of a simple scalar field theory: the φ4 field theory in d = 4 dimensions. However, all the fundamental difficulties of ... More


The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

Robert W. Batterman

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195146479
eISBN:
9780199833078
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0195146476.001.0001
Subject:
Philosophy, Philosophy of Science

This book focuses on a form of reasoning in science that I call “asymptotic reasoning.” At base, this type of reasoning involves methods that eliminate details and, in some sense, precision. ... More


The Theory Of QCD

GÜNTHER DISSERTORI, IAN G. KNOWLES, and MICHAEL SCHMELLING

in Quantum Chromodynamics: High Energy Experiments and Theory

Published in print:
2009
Published Online:
January 2010
ISBN:
9780199566419
eISBN:
9780191708060
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566419.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter begins with the formal derivation of QCD as a gauge theory based on the symmetry group SU(3). It then describes the basic reactions of lepton-lepton, lepton-hadron, and hadron-hadron ... More


THE WEYL ANOMALY AND RENORMALIZATION GROUP

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the quantum anomaly associated with the scale transformation of space-time coordinates, or the transformation generally called the Weyl transformation. In flat space-time, this ... More


Dimensional Regularization, Minimal Subtraction: RG Functions

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the concept of renormalization by minimal subtraction, within the framework of dimensional regularization. It first discusses the structure of renormalization constants and ... More


Renormalization group and problem of radiation

Israel Michael Sigal

in Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199652495
eISBN:
9780191741203
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652495.003.0012
Subject:
Physics, Atomic, Laser, and Optical Physics

The standard model of non-relativistic quantum electrodynamics describes non-relativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this ... More


Quantum field theory and the renormalization group

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a brief history of the origin and development of quantum field theory, and of the evolution of the interpretation of renormalization and the renormalization group which has led ... More


Scales III: Short-distance structure of quantum field theory

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199573264
eISBN:
9780191743313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573264.003.0018
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses one of the most fertile manifestations of scale separation in field theory: the Wilson operator product expansion (OPE), which provides a precise characterization of the ... More


Functional renormalization group

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter describes a general approach to the renormalization group (RG) close to ideas initially developed by Wegner and Wilson, and based on a partial integration over the large-momentum modes ... More


FLUCTUATION THERMODYNAMICS

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the Ginzburg-Landau functional and provides a general description of fluctuation thermodynamics within the framework of the functional integration over the fluctuation fields ... More


Phase transitions and critical phenomena

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

As an introduction to the physics of phase transitions and critical phenomena, this chapter explains a number of basic and fundamental ideas such as phases, phase transitions, phase diagrams, ... More


The s 4 field theory near dimension 4

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explains how the asymptotic renormalization group equations (RGE), introduced without too much justification in Section 10.6, can be proved within the framework of statistical (or ... More


General Renormalization Group. The Critical Theory Near Dimension Four

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0025
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The RG theory, as applied to Critical Phenomena, has been developed by Kadano, Wilson, Wegner, and many others. This chapter first describes the basic renormalization group ideas in a somewhat ... More


Asymptotic Explanation

Robert W. Batterman

in The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195146479
eISBN:
9780199833078
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195146476.003.0004
Subject:
Philosophy, Philosophy of Science

This chapter provides a fairly detailed discussion of the renormalization group account of the universality of critical phenomena. This discussion allows one to determine the distinctive features of ... More


Hierarchies, Complex Fractal Dimensions, and Log-Periodicity

Didier Sornette

in Why Stock Markets Crash: Critical Events in Complex Financial Systems

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175959
eISBN:
9781400885091
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175959.003.0006
Subject:
Business and Management, Finance, Accounting, and Banking

This chapter describes the concept of fractals and their self-similarity, including fractals with complex dimensions. It shows how these geometric and mathematical objects enable one to codify the ... More


Move to UCLA and continuing concerns

JAGDISH MEHRA and KIMBALL A. MILTON

in Climbing the Mountain: The Scientific Biography of Julian Schwinger

Published in print:
2003
Published Online:
February 2010
ISBN:
9780198527459
eISBN:
9780191709593
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527459.003.0014
Subject:
Physics, History of Physics

Julian Schwinger left Harvard University in 1971 to move to the University of California at Los Angeles (UCLA), perhaps because he perceived that his source theory had received a chilly reception at ... More


Renormalization group: General formulation

Jean Zinn-Justin

in Phase Transitions and Renormalization Group

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199227198
eISBN:
9780191711107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227198.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the general concept of renormalization group in the spirit of the work. It studies the role of fixed points and their stability properties. It exhibits a particular fixed ... More


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