Critical Phenomena: a Reminder / 1: |
Phase Diagrams and Critical Exponents / 1.1: |
Scale Invariance and Scaling Relations / 1.2: |
Some Simple Spin Systems / 1.3: |
Ising Model / 1.3.1: |
Tricritical Ising Model / 1.3.2: |
q-States Potts Model / 1.3.3: |
Vector Potts Model / 1.3.4: |
XY Model / 1.3.5: |
Yang-Lee Edge Singularity / 1.3.6: |
Percolation / 1.3.7: |
Linear Polymers / 1.3.8: |
Restricted Solid-On-Solid Models / 1.3.9: |
Some Experimental Examples / 1.4: |
Correspondence Between Statistical Systems and Field Theory / 1.5: |
Correspondence of Physical Quantities / 1.6: |
Free Energy Density / 1.6.1: |
Correlation Functions / 1.6.2: |
Correlation Lengths / 1.6.3: |
Conformal Invariance / 2: |
From Scale Invariance to Conformal Invariance / 2.1: |
Conformal Transformations in d Dimensions / 2.2: |
Conformal Transformations in Two Dimensions / 2.3: |
Conformal Invariance in Two Dimensions / 2.4: |
Correlation Functions of Quasi-primary Operators / 2.5: |
The Energy-Momentum Tensor / 2.6: |
Finite-Size Scaling / 3: |
Statistical Systems in Finite Geometries / 3.1: |
Finite-Size Scaling Hypothesis / 3.2: |
Universality / 3.3: |
Phenomenological Renormalization / 3.4: |
Consequences of Conformal Invariance / 3.5: |
Comparison with Experiments / 3.6: |
Representation Theory of the Virasoro Algebra / 4: |
Verma Module / 4.1: |
Hilbert Space Structure / 4.2: |
Null Vectors / 4.3: |
Kac Formula and Unitarity / 4.4: |
Minimal Characters / 4.5: |
Correlators, Null Vectors and Operator Algebra / 5: |
Null Vectors and Correlation Functions / 5.1: |
Operator Algebra and Associativity / 5.2: |
Analyticity and the Monodromy Problem / 5.3: |
Riemann's Method / 5.4: |
Ising Model Correlators / 6: |
Spin-Density Four-Point Function / 6.1: |
Energy-Density Four-Point Function / 6.2: |
Mixed Four-Point Functions / 6.3: |
Semi-Local Four-Point Functions / 6.4: |
Coulomb Gas Realization / 7: |
The Free Bosonic Scalar Field / 7.1: |
Screened Coulomb Gas / 7.2: |
Minimal Correlation Functions / 7.3: |
Minimal Algebras and OPE Coefficients / 7.4: |
The Hamiltonian Limit and Universality / 8: |
Hamiltonian Limit in the Ising Model / 8.1: |
Hubbard-Stratonovich Transformation / 8.2: |
Hamiltonian Spectrum and Conformal Invariance / 8.3: |
Temperley-Lieb Algebra / 8.5: |
Laudau-Ginzburg Classification / 8.6: |
Numerical Techniques / 9: |
Simple Properties of Quantum Hamiltonians / 9.1: |
Some Further Physical Quantities and their Critical Exponents / 9.2: |
Translation Invariance / 9.3: |
Diagonalization / 9.4: |
Extrapolation / 9.5: |
VBS Algorithm / 9.5.1: |
BST Algorithm / 9.5.2: |
The DMRG Algorithm / 9.6: |
Conformal Invariance in the Ising Quantum Chain / 10: |
Exact Diagonalization / 10.1: |
General Remarks / 10.1.1: |
Jordan-Wigner Transformation / 10.1.2: |
Diagonalization of a Quadratic Form / 10.1.3: |
Eigenvalue Spectrum and Normalization / 10.1.4: |
Character Functions |
Finite-Size Scaling Analysis / 10.2: |
Ground State Energy / 10.3.1: |
Operator Content / 10.3.2: |
Finite-Size Corrections / 10.3.3: |
Finite-Size Scaling Functions / 10.3.4: |
The Spin I Quantum Chain / 10.3: |
The Virasoro Generators / 10.4: |
Recapitulation / 10.5: |
Modular Invariance / 11: |
The Modular Group / 11.1: |
Implementation for Minimal Models / 11.2: |
Modular Invariance at c =1 / 11.3: |
Circle or Coulomb Models / 11.3.1: |
Orbifold Models / 11.3.2: |
Lattice Realizations / 11.4: |
Further Developments and Applications / 12: |
Three-States Potts Model / 12.1: |
Supersymmetry and Superconformal Invariance / 12.2: |
Ashkin Teller Model / 12.3: |
Relation with the XXZ Quantum Chain / 12.4.1: |
Global Symmetry and Boundary Conditions / 12.4.2: |
Phase Diagram / 12.4.3: |
Operator Content on the c =1 Line / 12.4.4: |
XXZ Quantum Chain / 12.5: |
Ising Correlation Functions on Cylinders / 12.7: |
Alternative Realizations of the Conformal Algebra / 12.8: |
Logarithmic Conformal Theories / 12.8.1: |
Lattice Two-Point Functions / 12.8.2: |
Polymers / 12.9: |
Lattice Animals / 12.10.1: |
A Sketch of Conformal Turbulence / 12.11: |
Some Remarks on 3D Systems / 12.12: |
Conformal Perturbation Theory / 13: |
Correlation Functions in the Strip Geometry / 13.1: |
General Remarks on Corrections to the Critical Behaviour / 13.2: |
Tower of the Identity / 13.3: |
Application to the Ising Model / 13.3.2: |
Application to the Three-States Potts Model / 13.3.3: |
Checking the Operator Content from Finite-Size Corrections / 13.3.4: |
Ising Model: Thermal Perturbation / 13.4: |
Ising Model: Magnetic Perturbation / 13.4.2: |
Truncation Method / 13.5: |
The Vicinity of the Critical Point / 14: |
The c-Theorem / 14.1: |
Application to Polymers / 14.1.1: |
Conserved Currents Close to Criticality / 14.2: |
Exact S-Matrix Approach / 14.3: |
Phenomenological Consequences / 14.4: |
Integrable Perturbations / 14.4.1: |
Universal Critical Amplitude Ratios / 14.4.2: |
Chiral Potts Model / 14.4.3: |
Oriented Interacting Polymers / 14.4.4: |
Non-integrable Perturbations / 14.4.5: |
Asymptotic Finite-Size Scaling Functions / 14.5: |
Surface Critical Phenomena / 15: |
Systems with a Boundary / 15.1: |
Conformal Invariance Close to a Free Surface / 15.2: |
Finite-Size Scaling with Free Boundary Conditions / 15.3: |
Surface Operator Content / 15.4: |
Temperley-Lieb Algebra and Relation with the XXZ Chain / 15.4.1: |
Ashkin-Teller Model / 15.4.4: |
Profiles / 15.4.7: |
Defect Lines |
Aperiodically Modulated Systems / 15.6.1: |
Persistent Currents in Small Rings / 15.6.2: |
Strongly Anisotropic Scaling / 16: |
Dynamical Scaling / 16.1: |
Schrödinger Invariance / 16.2: |
Towards Local Scale Invariance for General ? / 16.3: |
Some Remarks on Reaction-Diffusion Processes / 16.4: |
Anhang/Annexe |
List of Tables |
List of Figures |
References |
Index |
Critical Phenomena: a Reminder / 1: |
Phase Diagrams and Critical Exponents / 1.1: |
Scale Invariance and Scaling Relations / 1.2: |