The Kondo Problem to Heavy Fermions (Cambridge Studies in Magnetism, 2)

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The Kondo Problem to Heavy Fermions (Cambridge Studies in Magnetism, 2)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 444 p.
  • 言語 ENG
  • 商品コード 9780521599474
  • DDC分類 530.412

基本説明

New in paperback. Hardcover was published in 1993. Treats the anomalous behaviour associated with magnetic impurities in metals; the Kondo problem.

Full Description


The behaviour of magnetic impurities in metals has posed problems to challenge the condensed matter theorist over the past 30 years. This book deals with the concepts and techniques which have been developed to meet this challenge, and with their application to the interpretation of experiments. This book will be of interest to condensed matter physicists, particularly those interested in strong correlation problems. The detailed discussions of advanced many-body techniques should make it of interest to theoretical physicists in general.

Table of Contents

Preface                                            xi  (4)
Preface to paperbck edition xv (2)
Brief History xvii
1 Models of Magnetic Impurities 1 (28)
1.1 First Principles Model 1 (3)
1.2 Potential Scattering Model and the 4 (4)
Friedel Sum Rule
1.3 Virtual Bound States 8 (3)
1.4 The Non-Interacting Anderson Model 11 (5)
1.5 The s-d Exchange Model 16 (1)
1.6 The Anderson Model (U O) 17 (2)
1.7 Relation between the Anderson Model 19 (2)
and s-d Models
1.8 Parameter Regimes of the Anderson Model 21 (2)
1.9 The Ionic Model 23 (4)
1.10 The Coqblin-Schrieffer Model 27 (2)
2 Resistivity Calculations and the 29 (18)
Resistance Minimum
2.1 Multiple Impurity Scattering 29 (3)
2.2 Conductivity and the Boltzmann Equation 32 (2)
2.3 Conductivity and Linear Response Theory 34 (4)
2.4 Kondo's Explanation of the Resistance 38 (9)
Minimum
3 The Kondo Problem 47 (24)
3.1 Perturbation Theory 47 (3)
3.2 Beyond Perturbation Theory 50 (8)
3.3 Poor Man's Scaling 58 (7)
3.4 Scaling for the Anderson Model 65 (6)
4 Renormalization Group Calculations 71 (32)
4.1 The Renormalization Group 71 (4)
4.2 Linear Chain Form for the s-d Model 75 (3)
4.3 Logarithmic Discretization 78 (3)
4.4 The Numerical Renormalization Group 81 (4)
Calculations
4.5 Effective Hamiltonians near the Fixed 85 (2)
Points
4.6 High and Low Temperature Results 87 (6)
4.7 The Symmetric Anderson Model 93 (5)
4.8 The Asymmetric Anderson Model 98 (5)
5 Fermi Liquid Theories 103 (32)
5.1 Phenomenological Fermi Liquid Theory 103 (7)
5.2 The Generalized Friedel Sum Rule 110 (5)
5.3 Microscopic Fermi Liquid Theory 115 (6)
5.4 The Electrical Conductivity 121 (5)
5.5 Finite Order Perturbation Results 126 (4)
5.6 Renormalization Group Results for 130 (5)
Spectral Densities
6 Exact Solutions and the Bethe Ansatz 135 (36)
6.1 The Linear Dispersion s-d Model 135 (5)
6.2 Diagonalization of the s-d Model 140 (6)
6.3 Excitations 146 (5)
6.4 Thermodynamics for the s-d Model for S 151 (5)
= 1/2
6.5 Results for the s-d Model (S > 1/2) 156 (3)
6.6 Integrability of the Anderson Model 159 (6)
6.7 Results for the Symmetric Anderson 165 (3)
Model
6.8 Results for the Asymmetric Anderson 168 (3)
Model
7 N-fold Degenerate Models I 171 (34)
7.1 Introduction 171 (2)
7.2 Perturbation Theory and the 1/N 173 (7)
Expansion
7.3 Exact Results 180 (10)
7.4 Fermi Liquid Theories 190 (6)
7.5 Slave Bosons and Mean Field Theory 196 (9)
8 N-fold Degenerate Models II 205 (28)
8.1 Introduction 205 (1)
8.2 The Non-Crossing Approximation (NCA) 206 (7)
8.3 Beyond Mean Field Theory 213 (10)
8.4 The Variational 1/N Expansion 223 (10)
9 Theory and Experiment 233 (80)
9.1 Introduction 233 (2)
9.2 High Energy Spectroscopies 235 (12)
9.3 Thermodynamic Measurements 247 (26)
9.4 Transport Properties 273 (12)
9.5 Neutron Scattering 285 (6)
9.6 Local Measurements 291 (18)
9.7 The Possibility of First Principles 309 (4)
Calculations?
10 Strongly Correlated Fermions 313 (50)
10.1 Introduction 313 (2)
10.2 Anomalous Rare Earth Compounds 315 (8)
10.3 Heavy Fermions 323 (9)
10.4 Fermi Liquid Theory and Renormalized 332 (6)
Bands
10.5 Mean Field Theory 338 (9)
10.6 Further Theoretical Approaches 347 (7)
10.7 The High Tc Superconductors 354 (9)
Appendices 363 (56)
A Scattering Theory 363 (4)
B Linear Response Theory and Conductivity 367 (4)
Formulae
C The Zero Band Width Anderson Model 371 (4)
D Scaling Equations for the 375 (6)
Coqblin-Schrieffer Model
E Further Fermi Liquid Relations 381 (6)
F The Algebraic Bethe Ansatz 387 (4)
G The Wiener-Hopf Solution 391 (4)
H Rules for Diagrams 395 (4)
I Perturbational Results to Order 1/N 399 (4)
J The n-Channel Kondo Model for n > 2S 403 (2)
K Summary of Single Impurity Results 405 (6)
L Renormalized Perturbation Theory 411 (8)
Addendum 419 (8)
References 427 (12)
Index 439