CONTENTS -- Preface -- Introduction to the Non-Perturbative Renormalization Group Bertrand Delamotte -- Contents -- 1. Wilson's Renormalization Group -- 1.1. Introduction -- 1.2. The Perturbative Method in Field Theory -- 1.3. Wilson's Approach to the Renormalization Group -- 2. Renormalization Group Transformations -- 2.1. Blocks of Spins -- 2.2. Two Remarks Concerning RG Transformations -- 2.3. Linear RG Transformations and Correlation Length -- 3. Properties of the RG Flow: Fixed Points, Critical Surface, Relevant Directions -- 3.1. Scaling Relations - Linearization of the Flow Around the Fixed Point -- 3.2. The Correlation Length and the Spin-Spin Correlation Function -- 3.3. Scaling of the Correlation Function in the Presence of a Magnetic Field - Relation Among Exponents -- 3.4. The Example of the Two-Dimensional Ising Model on the Triangular Lattice -- 4. The Non-Perturbative Renormalization Group -- 4.1. Introduction -- 4.1.1. The Wilson-Polchinski Approach -- 4.2. The Effective Average Action Method -- 4.2.1. Block-Spins, Coarse Graining, Legendre Transform, etc. -- 4.3. An Integral Representation of Γk and the Limit k -- 5. The Exact RG Equation and Its Properties -- 5.1. Some General Properties of the Effective Average Action Method -- 6. Approximation Procedures -- 6.1. The Green Function Approach -- 6.2. The Derivative Expansion -- 7. The Local Potential Approximation for the Ising Model -- 7.1. The Flow Equation of the Potential -- 7.2. The Scaling Form of the RG Equation of the Dimensionless Potential -- 8. The Critical and Non-Critical Behaviour Model within the LPA -- 8.1. The Low and the High Temperature Phases -- 8.2. The Critical Point -- 8.3. The Critical Exponents -- 9. The O(N) Models at O(∂2) of the Derivative Expansion -- 9.1. The RG Equation for the Potential -- 9.2. The RG Equation for the Dimensionless Potential ˜U k.

9.3. The Limits d 4, d 2 and N -- 10. Conclusion -- Acknowledgements -- Appendix A. De.nitions, conventions -- Appendix B. The Exact RG equations -- Appendix B.1. RG equation for Wk[B] -- Appendix B.2. RG equation for Γk[M] -- Appendix B.3. RG equation for the e.ective potential -- References -- Introduction to Critical Dynamics Reinhard Folk -- Contents -- 1. Introduction -- 2. Experimental Evidence -- 2.1. Fluids -- 2.2. Light Scattering -- 2.3. Ferromagnets -- 2.4. Superfluid 4He -- 3. Van Hove Theory -- 4. Dynamical Scaling -- 4.1. Scaling Form of the Dynamic Susceptibility -- 4.2. Finding the Dynamical Exponent z by Scaling Relations -- 4.2.1. Ferromagnet -- 4.2.2. Fluids -- 4.2.3. Superfluid Transition -- 5. From Dynamic Equations to a Lagrangian -- 5.1. Static Functional -- 5.2. Dynamic Equations -- 5.3. Dynamic Functional -- 5.4. Renormalization -- 6. Renormalization and the Dynamical Exponent -- 6.1. Structure and Renormalization -- 6.2. Calculating the Dynamical Exponent -- 6.2.1. Models without Mode Coupling Terms -- 6.2.2. Models with Mode Coupling Terms -- 7. Comparison with Experiment -- 7.1. General Procedure -- 7.2. Fluids: The Linewidth in Light Scattering -- 7.2.1. Theoretical Result in One Loop Order -- 7.2.2. Limiting behaviour -- 7.2.3. Remarks on the Shear Viscosity -- 7.3. Ferromagnets: The Shape Function -- 7.4. Superfluid Transition: The Thermal Conductivity -- Acknowledgements -- References -- Spacetime Approach to Phase Transitions Wolfhard Janke and Adriaan M. J. Schakel -- Contents -- 1. Introduction -- 2. Lattice Field Theory -- 2.1. Noninteracting Theory -- 2.2. Loop Gas -- 2.3.

3.6. Summary -- 4. Monte Carlo Simulations -- 4.1. Plaquette Update -- 4.2. Numerical Results -- 4.3. Summary -- 5. Further Applications -- 5.1. Higgs Model -- 5.2. Bose-Einstein Condensation -- 5.3. Summary -- 6. Dual Theories -- 6.1. Peierls Domain Walls -- 6.2. Vortex Lines -- 6.3. Monopole Loops -- 6.4. Summary -- Acknowledgements -- References -- Representations of Self-Organized Criticality Alexander Olemskoi and Dmytro Kharchenko -- Contents -- 1. Introduction -- 2. Brief Overview of Approaches for Self-Organized Criticality -- 3. Synergetic Concept -- 3.1. Self-Consistent Approach -- 3.1.1. Mechanistic Model of the Sandpile -- 3.1.2. Noise Influence on Avalanche Formation -- 3.1.3. Generalized Model -- 3.2. Self-Similarity of the Avalanche Ensemble -- 4. Euclidean Field Approach and Optimal Trajectories -- 4.1. Variational Principle -- 4.2. Dynamics of the System Exhibiting SOC -- 4.2.1. Pure White Noise -- 4.2.2. Coloured Noise -- 5. Scaling Properties of the System with SOC -- References -- Phase Transitions in the Pseudospin-Electron Model Ihor Stasyuk -- Contents -- 1. Introduction -- 2. Thermodynamics of Simpli.ed PEM in Dynamical Mean Field Theory -- 3. Simplified PEM in Generalized Random Phase Approximation -- 3.1. Strong Coupling Case -- U = 0, . = 0 -- 3.1.1. Thermodynamics of the Uniform State -- 3.1.2. The Chess-Board Phase -- 3.2. Weak Coupling Case -- U = 0 -- 3.2.1. Uniform Phase -- 3.2.2. Phase with Double Modulation -- 3.2.3. Pair Correlation Function and Susceptibilities -- 3.3. Superconductivity in the PEM -- 4. Thermodynamics of PEM at Finite U Values -- the U Limit -- 5. Two-Sublattice Pseudospin-Electron Model -- 6. Conclusions -- Acknowledgements -- References -- Index.