## Lectures on Phase Transitions and the Renormalization GroupCovering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book. |

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### Contents

1 | |

23 | |

How Phase Transitions Occur in Practice | 85 |

Critical Phenomena in Fluids | 117 |

Landau Theory | 135 |

Fluctuations and the Breakdown | 167 |

Exercises | 185 |

Anomalous Dimensions 189 | 189 |

Scaling in Static Dynamic and NonEquilibrium | 201 |

The Renormalisation Group | 229 |

Anomalous Dimensions Far From Equilibrium | 287 |

Continuous Symmetry | 335 |

Critical Phenomena Near Four Dimensions | 351 |

Index | 389 |

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### Common terms and phrases

anomalous dimension Barenblatt's equation block spin calculation chapter coarse-grained configuration consider correlation function correlation length corresponding coupling constants critical behaviour critical exponents critical fixed point critical phenomena critical point defined degrees of freedom depends differential dimensional analysis discussion diverges dynamics effective Hamiltonian eigenvalues equilibrium ergodic regions example external field ferromagnet finite fluctuations fluid free energy density Gaussian approximation given Hamiltonian Hence implies interactions intermediate asymptotic Ising model Landau free energy Landau theory lattice length scale long range order magnetic magnetisation mean field theory microscopic non-zero obtain order parameter particles partition function perturbation theory phase diagram phase space phase transition Phys physical polymer problem quantity quantum recursion relations renormalisation renormalisation group result RG transformation scaling function scaling hypothesis scaling law singular spatial statistical mechanics temperature term theorem thermodynamic limit tion transfer matrix two-point correlation function variables write zero

### Popular passages

Page ix - The enormous growth in the number of physicists has tended to make the familiar channels of communication considerably less effective. It has become increasingly difficult for experts in a given field to keep up with the current literature; the novice can only be confused. What is needed is both a consistent account of a field and the presentation of a definite "point of view

Page iii - Frontiers in Physics David Pines, Editor Volumes of the Series published from 1961 to 1973 are not officially numbered. The parenthetical numbers shown are designed to aid librarians and bibliographers to check the completeness of their holdings. Titles published in this series prior to 1987 appear under either the WA Benjamin or the Benjamin/Cummings imprint; titles published since 1986 appear under the Addison-Wesley imprint.

Page ix - ... point of view" concerning it. Formal monographs cannot meet such a need in a rapidly developing field, and, perhaps more important, the review article seems to have fallen into disfavor. Indeed, it would seem that the people most actively engaged in developing a given field are the people least likely to write at length about it. "Frontiers in Physics" has been conceived in an effort to improve the situation in several ways.

Page ix - Indeed, it would seem that the people who are most actively engaged in developing a given field are the people least likely to write at length about it. Frontiers in Physics was conceived in 1961 in an effort to improve the situation in several ways. Leading physicists frequently give a series of lectures, a graduate seminar, or a graduate course in their special fields of interest. Such lectures serve to summarize the present status of a rapidly developing field and may well constitute the only...

Page iv - Current, 1967 Current Algebras and Applications to Particle Physics, 1968 Nuclear Theory: The Quasiparticle Method, 1968 The Quark Model, 1969 Approximation Methods in Quantum Mechanics, 1969 Nonlinear Plasma Theory, 1969 Quantum Kinematics and Dynamics, 1970 Statistical Mechanics: A Set of Lectures...

Page ix - Frontiers in Physics" has been conceived in an effort to improve the situation in several ways. First, to take advantage of the fact that the leading physicists today frequently give a series of lectures, a graduate seminar, or a graduate course in their special fields of interest. Such lectures serve to summarize the present status of a rapidly developing field and may well constitute the only coherent account available at the time. Often, notes on lectures exist (prepared by the lecturer...

Page iii - A Lecture Note and Reprint Volume, 1961 Quantum Electrodynamics: A Lecture Note and Reprint Volume The Theory of Fundamental Processes: A Lecture Note Volume, 1961 Problem in Quantum Theory of Many,Particle Systems: A Lecture Note and Reprint Volume, 1961 The Many-Body Problem: A Lecture Note and Reprint Volume, 1961 The Mossbauer Effect: A Review — With a Collection of Reprints, 1962 Quantum Statistical Mechanics: Green's Function Methods in Equilibrium and Nonequilibrium Problems, 1962 Paramagnetic...

Page iv - Dual Resonance Models, 1974 Modern Theory of Critical Phenomena, 1976 Hydrodynamic Fluctuation, Broken Symmetry, and Correlation Functions, 1975 Qualitative Methods in Quantum Theory, 1977 Condensed Matter Physics: Dynamic Correlations, 1980 Gauge Fields: Introduction to Quantum Theory, 1980 Field Theory: A Modern Primer, 1981 [cf. 74— 2nd ed.] Heavy Ion Reactions: Lecture Notes Vol.

Page iv - Interactions, 1972 Combinatorics and Renormalization in Quantum Field Theory, 1973 The Redshift Controversy, 1973 Hadron Physics at Very High Energies, 1973 Basic Principles of Plasma Physics: A Statistical Approach, 1973 (2nd printing, with revisions, 1980) The Physical Principles of Electron Paramagnetic Resonance, 2nd Edition, completely revised, enlarged, and reset, 1973 [cf. (9)— 1st edition] Volumes published from 1 974 onward are being numbered as an integral part of the bibliography.

Page iii - Correlations to Collective Motion, 1964 Mandelstam Theory and Regge Poles: An Introduction for Experimentalists, 1963 Complex Angular Momenta and Particle Physics: A Lecture Note and Reprint Volume, 1963 The Equilibrium Theory of Classical Fluids: A Lecture Note and Reprint Volume, 1964 The Eightfold Way (A Review — With a Collection of Reprints), 1964 Strong-Interaction Physics: A Lecture Note Volume, 1964 Theory of Interacting Fermi Systems, 1964 Theory...