Defects and geometry in condensed matter physics / David R. Nelson.

Format:

Book

Author/Creator:

Nelson, David R., 1951-

Language:

English

Subjects (All):

Condensed matter--Defects.

Condensed matter.

Physical Description:

xiii, 377 pages : illustrations ; 26 cm

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2002.

Summary:

A pedagogic graduate level introduction to the field of defects and geometry.

Contents:

1 Fluctuations, renormalization and universality 1

1.1 Fluctuations and universality in condensed matter physics 2

1.2 The universal Prandtl number in two-dimensional hydrodynamics 5

1.3 The universal Poisson ratio in fluctuating polymerized membranes 8

1.4 Defect-mediated phase transitions and hydrodynamic theories 12

1.5 The contents of this book 18

Appendix A Renormalization 21

Appendix B The self-dual point of Ising spins in two dimensions 26

2 Defect-mediated phase transitions 30

2.2 The XY model and superfluidity in two dimensions 41

2.3 Dynamic scaling and third sound in helium films 60

2.4 Statistical mechanics of two-dimensional melting 68

2.5 Melting dynamics 91

2.6 Anisotropic melting 99

2.7 Line singularities in three dimensions 106

3 Order, frustration and two-dimensional glass 124

3.2 Order and frustration in quenched binary arrays 129

3.3 Order and frustration in spaces of incommensurate curvature 136

4 The structure and statistical mechanics of three-dimensional glass 146

4.1 A physical picture 147

4.2 The model free energy 154

5 The statistical mechanics of crumpled membranes 165

5.1 Flat surfaces 166

5.2 Crumpled membranes 170

5.3 Normal-normal correlations in liquid membranes 179

5.4 Tethered surfaces with bending energy 181

5.5 Defects and hexatic order in membranes 186

6 Defects in superfluids, superconductors and membranes 194

6.2 Two-dimensional superfluids and superconductors 198

6.3 Defects in membranes and monolayers 217

Appendix A Superfluid density and momentum correlations 238

7 Vortex-line fluctuations in superconductors from elementary quantum mechanics 245

7.2 Correlated pinning and quantum bound states 249

7.3 Flux melting and the quantum harmonic oscillator 258

7.4 Vortex entanglement in the liquid phase 261

Appendix A The transfer-matrix representation of the partition function 266

Appendix B Vortex probability distributions 267

8 Correlations and transport in vortex liquids 271

8.2 Statistical mechanics of flexible lines 285

8.3 Correlations in flux liquids with weak disorder 301

8.4 Dynamics near the irreversibility line 311

9 Statistical mechanics of directed polymers 322

9.2 One polymer in a nematic solvent 327

9.3 A model of polymer nematics 332

9.4 Mapping onto boson quantum mechanics 335

9.5 Correlations in polymer nematics with soft broken symmetry 341

9.6 The hydrodynamic treatment of line liquids 344

9.7 Defects in hexagonal columnar crystals 347.

Notes:

Includes bibliographical references and index.

ISBN:

0521801591

0521004004

OCLC:

46473940