LEADER 05146oam 2200589 450 001 9910779991003321 005 20190911112728.0 010 $a981-4417-64-5 035 $a(OCoLC)856447075 035 $a(MiFhGG)GVRL8RHB 035 $a(EXLCZ)992550000001107668 100 $a20130927h20132013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$a40 years of Berezinskii-Kosterlitz-Thouless theory /$feditor, Jorge V. Jose, Indiana University, USA 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$d2013 210 1$aNew Jersey :$cWorld Scientific,$d[2013] 210 4$d?2013 215 $a1 online resource (xii, 351 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a981-4417-62-9 311 $a1-299-77076-2 320 $aIncludes bibliographical references and index. 327 $aContents; 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 327 $a1.6.1. 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 327 $a2.4. 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 327 $a3.3. 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 327 $aAppendix 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 327 $a5. Berezinskii-Kosterlitz-Thouless Transition within the Sine-Gordon Approach: The Role of the Vortex-Core Energy L. Benfatto, C. Castellani and T. Giamarchi 330 $aOn 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 606 $aCondensed matter 606 $aSolid state physics 606 $aNuclear physics 606 $aStatistical physics 615 0$aCondensed matter. 615 0$aSolid state physics. 615 0$aNuclear physics. 615 0$aStatistical physics. 676 $a530.41 686 $a33.26$2bcl 686 $a33.74$2bcl 702 $aJose$b Jorge V. 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910779991003321 996 $a40 years of Berezinskii-Kosterlitz-Thouless theory$93870989 997 $aUNINA