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Physics of Critical Fluctuations Yuli M. Ivanchenko

Physics of Critical Fluctuations By Yuli M. Ivanchenko

Physics of Critical Fluctuations by Yuli M. Ivanchenko


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Summary

Building on Wilson's renormalization group, the authors have developed a unified approach that not only reproduces known results but also yields new results.

Physics of Critical Fluctuations Summary

Physics of Critical Fluctuations by Yuli M. Ivanchenko

Building on Wilson's renormalization group, the authors have developed a unified approach that not only reproduces known results but also yields new results. A systematic exposition of the contemporary theory of phase transitions, the book includes detailed discussions of phenomena in Heisenberg magnets, granular super-conducting alloys, anisotropic systems of dipoles, and liquid-vapor transitions. Suitable for advanced undergraduates as well as graduate students in physics, the text assumes some knowledge of statistical mechanics, but is otherwise self-contained.

Table of Contents

1. Classical Approach.- 1.1 Introduction.- 1.2 Landau Theory.- 1.3 Broken Symmetry and Condensation.- 1.4 Ergodicity.- 1.5 Gaussian Approximation.- 1.6 The Ginzburg Criterion.- 1.7 The Scaling Hypothesis.- 2 The Ginzburg-Landau Functional.- 2.1 Introduction.- 2.2 Classical Systems.- 2.3 Quantum Systems.- 3 Wilsons Renormalization Scheme.- 3.1 Introduction.- 3.2 Kadanoffs Invariance.- 3.3 Wilsons Theory.- 4 Field Theoretical RG.- 4.1 Introduction.- 4.2 Perturbation Theory.- 4.3 Renormalization.- 4.4 Scaling Laws.- 4.5 ?-Expansion.- 4.6 Expansions at d = 3.- 4.7 Results of Different Approaches.- 5 Generalized RG Approach.- 5.1 Introduction.- 5.2 Scale Transformations.- 5.3 Scale Equations.- 5.4 RG Equations.- 5.5 Applications of Generalized SE.- 5.6 ?-Expansion.- 5.7 Comparison of Different RG Approaches.- 6 RG Study of Particular Systems.- 6.1 Reduction of the Characteristic Set.- 6.2 The Gaussian Model.- 6.3 The 4 Model.- 6.4 The 4+6-Model.- 6.5 Free Energy in the Critical Region.- 7 Competing Interactions.- 7.1 Heisenberg Magnets.- 7.2 Bicritical Points in Antiferromagnets.- 7.3 Dipole Interaction.- 7.4 Impure Systems.- 8 Exactly Solvable Models and RG.- 8.1 Fluctuation Effects in Spherical Model.- 8.2 Inversion of Phase Transitions.- 8.3 Model with Reduced Interaction.- 8.4 First-Order Transitions.- 8.5 RG and Reduced Interactions.- 9 Application to Copper Oxides.- 9.1 Introduction.- 9.2 La2CuO4 Systems.- 9.3 Oxygen Ordering in ABa2Cu3O6+x.- 9.4 d-Pairing in the Superconducting State.- A Evaluation of Integrals.- A.1 Gaussian Integral.- A.2 A Typical Diagram.- B Local RG.- B.1 General Consideration.- B.2 Spectral Theorems.

Additional information

NPB9780387944142
9780387944142
0387944141
Physics of Critical Fluctuations by Yuli M. Ivanchenko
New
Hardback
Springer-Verlag New York Inc.
1995-09-21
390
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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