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

Format:

Book

Contributor:

Holovatch, Yurij.

Series:

Advanced Problems of Phase Transition Theory

Advanced Problems of Phase Transition Theory ; v.2

Language:

English

Subjects (All):

Phase transformations (Statistical physics).

Statistical physics.

Physical Description:

1 online resource (308 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, NJ ; London : World Scientific, 2007.

Language Note:

English

Summary:

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

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611918590

9781281918598

1281918598

9789812708762

9812708766

OCLC:

747539595