Overview
- Nominated as an outstanding Ph.D. thesis by the University of Oxford, UK
- Offers a broad perspective on the application of loop models to critical phenomena
- Relevant to quantum magnetism, disordered systems and polymer physics
- Introduces new types of geometrical phase transition
- Advances our understanding of the relation between field theory and random geometry
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Theses (Springer Theses)
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Table of contents (7 chapters)
Keywords
About this book
When close to a continuous phase transition, many physical systems can usefully be mapped to ensembles of fluctuating loops, which might represent for example polymer rings, or line defects in a lattice magnet, or worldlines of quantum particles.
'Loop models' provide a unifying geometric language for problems of this kind.
This thesis aims to extend this language in two directions. The first part of the thesis tackles ensembles of loops in three dimensions, and relates them to the statistical properties of line defects in disordered media and to critical phenomena in two-dimensional quantum magnets. The second part concerns two-dimensional loop models that lie outside the standard paradigms: new types of critical point are found, and new results given for the universal properties of polymer collapse transitions in two dimensions.
All of these problems are shown to be related to sigma models on complex or real projective space, CP^{n−1} or RP^{n−1} -- in some cases in a 'replica' limit -- and this thesis is also an in-depth investigation of critical behaviour in these field theories.
Authors and Affiliations
Bibliographic Information
Book Title: Critical Phenomena in Loop Models
Authors: Adam Nahum
Series Title: Springer Theses
DOI: https://doi.org/10.1007/978-3-319-06407-9
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-06406-2Published: 14 October 2014
Softcover ISBN: 978-3-319-36063-8Published: 22 September 2016
eBook ISBN: 978-3-319-06407-9Published: 01 October 2014
Series ISSN: 2190-5053
Series E-ISSN: 2190-5061
Edition Number: 1
Number of Pages: XVII, 141
Number of Illustrations: 2 b/w illustrations, 36 illustrations in colour
Topics: Mathematical Methods in Physics, Complex Systems, Mathematical Applications in the Physical Sciences, Condensed Matter Physics, Statistical Physics and Dynamical Systems