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Critical Phenomena in Loop Models

  • Adam Nahum

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Adam Nahum
    Pages 1-23
  3. Adam Nahum
    Pages 25-50
  4. Adam Nahum
    Pages 63-81
  5. Adam Nahum
    Pages 83-115
  6. Adam Nahum
    Pages 117-129
  7. Adam Nahum
    Pages 131-133
  8. Back Matter
    Pages 135-141

About this book

Introduction

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.

Keywords

CP^{n-1} Model Completely-packed Loop Model Deconfined Criticality Fractal Geometry Loop Gas Loop Models Polymer Collapse Random Geometry Replica Field Theory Replica Sigma Model Self-avoiding Trails Self-avoiding walk Vortex Lines Vortex Percolation

Authors and affiliations

  • Adam Nahum
    • 1
  1. 1.Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-06407-9
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-06406-2
  • Online ISBN 978-3-319-06407-9
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site