Physics of Critical Fluctuations

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.

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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 Wilson's Renormalization Scheme.- 3.1 Introduction.- 3.2 Kadanoff's Invariance.- 3.3 Wilson's 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 Ø4 Model.- 6.4 The Ø4+Ø6-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.