40 years of Berezinskii-Kosterlitz-Thouless theory / editor, Jorge V. Jose, Indiana University, USA.

Format:

Book

Contributor:

José, Jorge V. (Jorge Valenzuela), 1949- editor.

Series:

Gale eBooks

Language:

English

Subjects (All):

Condensed matter.

Solid state physics.

Nuclear physics.

Statistical physics.

Physical Description:

1 online resource (xii, 351 pages) : illustrations

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, 2013.

New Jersey : World Scientific, [2013]

Summary:

On the 40th anniversary of the Berezinskii-Kosterlitz-Thouless Theory (BKT), this informative volume looks back at some of the developments and achievements and varied physics applications which ensued from the beautiful BKT vortex-unbinding seminal idea.During the last four decades, BKT theory, which is undeniably one of the most important developments in condensed matter and theoretical physics of the second half of the twentieth century, has expanded widely. It has been used and extended from many different theoretical and experimental perspectives. New and unexpected features have been unc

Contents:

Contents; Introduction and Overview J. V. Jose; References; 1. Early Work on Defect Driven Phase Transitions J. M. Kosterlitz and D. J. Thouless; 1.1. Introduction; 1.2. One-Dimensional Ising Model; 1.3. Vortex Driven Transitions in Superfluid Films; 1.4. Other Systems with Defect-Mediated Transitions; 1.4.1. Two-dimensional magnetic systems; 1.4.2. Isotropic Heisenberg model; 1.4.3. Two-dimensional Coulomb plasma; 1.4.4. Two-dimensional crystals; 1.4.5. Thin film superconductors; 1.5. Scaling Theory; 1.6. Scaling Theory in Analogous Systems

1.6.1. Duality and the roughening of crystal facets1.6.2. Substrate effects; 1.6.3. Melting of a 2D crystal; 1.6.4. Substrate effects on 2D melting; 1.6.5. Scaling in superconducting films; 1.7. Experiments and Simulation; 1.7.1. Measurements on superfluid films; 1.7.2. Experimental measurements on 2D melting; 1.7.3. Simulations of 2D melting; References; 2. Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition J. V. Jose; 2.1. Introduction; 2.2. Duality Transformations in the 2D XY Model; 2.3. Migdal Kadanoff RG Approximation of the Two-Dimensional XY Model

2.4. Correlation Function Calculations and Renormalization Group Equations2.5. Symmetric Breaking Fields, Duality and RG Equations; 2.6. An Early Experimental Confirmation of the BKT Theory; 2.3. Conclusions; Acknowledgments; References; 3. Berezinskii-Kosterlitz-Thouless Transition through the Eyes of Duality G. Ortiz, E. Cobanera and Z. Nussinov; 3.1. Introduction; 3.2. The XY Model: A Paradigm of BKT Phenomenology; 3.2.1. A transfer operator for the XY model; 3.2.2. Hamiltonian form of the XY model; 3.2.3. Duality of the XY model without the Villain approximation

3.3. The p-Clock Model: A Close Relative of XY3.3.1. A transfer matrix for the p-clock model; 3.3.2. Hamiltonian form of the p-clock model; 3.3.3. Dualities of the p-clock model; 3.3.4. Self-dual classical p-clock model; 3.3.5. Exact and emergent symmetries of the p-clock model; 3.3.5.1. Non-Abelian, discrete symmetries; 3.3.5.2. Emergent U(1) symmetry; 3.4. Phase Diagram: From the p-Clock to the XY Model; Appendix A: Exponential of Shift Operators; Appendix B: Duality of the XY Model to q-Deformed Bosons; Appendix C: The Villain and Its Dual Solid-On-Solid Models

Appendix D: The p-Clock Model for p = 2, 3, and 4Appendix E: Peierls Argument for the p-Clock Model; References; 4. The Berezinskii-Kosterlitz-Thouless Transition in Superconductors A. M. Goldman; 4.1. Introduction; 4.2. Phenomenological Theory - Mostly Films; 4.3. Experimental Evidence - Films; 4.4. Phenomenological Theory - Arrays; 4.5. Experiments - Arrays; 4.6. Comments on Renormalization Effects; 4.7. Summary; Acknowledgments; References

5. Berezinskii-Kosterlitz-Thouless Transition within the Sine-Gordon Approach: The Role of the Vortex-Core Energy L. Benfatto, C. Castellani and T. Giamarchi

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789814417648

9814417645

OCLC:

856447075