Order, disorder and criticality [[electronic resource] ] . Volume 2 : advanced problems of phase transition theory / / editor, Yurij Holovatch

• Pubblicazione: Hackensack, NJ ; ; London, : World Scientific, 2007
• Descrizione fisica: 1 online resource (308 p.)
• Disciplina: 530.4/74
• Soggetto topico: Phase transformations (Statistical physics); Statistical physics
• Altri autori: HolovatchYurij
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 ; 9.2. The RG Equation for the Dimensionless Potential ̃U k9.3. The Limits d 4, d 2 and N; 10. Conclusion; Acknowledgements; Appendix A. Definitions, 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 elective 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. Super fluid 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
• Sommario/riassunto: This book is the second volume of review papers on advanced problems of phase transitions and critical phenomena, following the success of the first volume in 2004. Broadly, the volume aims to demonstrate that the phase transition theory, which experienced its 'golden age' during the 70's and 80's, is far from over and there is still a good deal of work to be done, both at the fundamental level and in respect of applications.The topics presented in this volume include: critical behavior as explained by the non-perturbative renormalization group, critical dynamics, a spacetime approach to phase t
• Titolo autorizzato: Order, disorder and criticality
• ISBN: 1-281-91859-8; 9786611918590; 981-270-876-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910784750603321
• Lo trovi qui: Univ. Federico II
• Serie: Advanced Problems of Phase Transition Theory