Defects and Geometry in Condensed Matter Physics

Thermally excited defects such as vortices, disclinations, dislocations, vacancies and interstitials play a key role in the physics of crystals, superfluids, superconductors, liquid crystals and polymer arrays. Geometrical aspects of statistical mechanics become particularly important when thermal fluctuations entangle or crumple extended line-like or surface-like objects in three dimensions. In the case of entangled vortices above the first-order flux lattice melting transition in high temperature superconductors, the lines themselves are defects. A variety of low temperature theories combined with renormalization group ideas are used to describe the delicate interplay between defects, statistical mechanics and geometry characteristic of these problems in condensed matter physics. In this 2002 book, David Nelson provides a coherent and pedagogic graduate level introduction to the field of defects and geometry.

Table of Contents:
1. Fluctuations, renormalization and universality; 2. Defect mediated phase transitions; 3. Order, frustration; 4. The structure and statistical mechanics of glass; 5. The statistical mechanics of crumpled membranes; 6. Defects in superfluids, superconductors and membranes; 7. Vortex line fluctuations in superconductors from elementary quantum mechanics; 8. Correlations and transport in vortex liquids; 9. The statistical mechanics of directed polymers.

About the Author :
David Nelson is Mallinckrodt Professor of Physics and Professor of Applied Physics at Harvard University. He received his Ph.D. in 1975 from Cornell University. His research focuses on collective effects in the physics of condensed matter, particularly on the interplay between fluctuations, geometry and statistical mechanics. In collaboration with his Harvard colleague, Bertrand I. Halperin, he is responsible for a theory of dislocation- and disclination-mediated melting in two dimensions. The prediction of Halperin and Nelson of a fourth 'hexatic' phase of matter, interposed between the usual solid and liquid phases, has now been confirmed in many experiments on thin films and bulk materials. A member of the National Academy of Sciences, the American Academy of Arts and Sciences and a Fellow of the American Physical Society, David Nelson has been an A. P. Sloan Fellow, a Guggenheim Fellow and a Junior and Senior Fellow in the Harvard Society of Fellows. He is the recipient of a five-year MacArthur Prize Fellowship, the National Academy of Sciences Prize for Initiatives in Research, and the Harvard Ledlie Prize.

Review :
'For 25 years, David Nelson has made major contributions to the study of how condensed matter systems as solids, liquid crystals, superfluids, and polymer solutions and melts. His dominance in the field has been reinforced by his excellent surveys in the proceedings of summer schools, workshops, and conferences from 1983 to 1996. The book provides an admirable overview of Nelson's achievements and of their relation to other work.' Physics Today