Critical Phenomena in Loop Models - Springer Theses - Adam Nahum - Books - Springer International Publishing AG - 9783319064062 - October 14, 2014
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Adam Nahum
Critical Phenomena in Loop Models - Springer Theses 2015 edition

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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 world lines 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.

158 pages, 2 black & white illustrations, 36 colour illustrations, biography

Media Books     Hardcover Book   (Book with hard spine and cover)
Released October 14, 2014
ISBN13 9783319064062
Publishers Springer International Publishing AG
Pages 141
Dimensions 172 × 245 × 14 mm   ·   386 g
Language English  

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