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Critical Phenomena in Loop Models

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Critical Phenomena in Loop Models/ by Adam Nahum.
Author:	Nahum, Adam.
Description:	XVII, 141 p. 38 illus., 36 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Physics. -
Online resource:	https://doi.org/10.1007/978-3-319-06407-9
ISBN:	9783319064079

Critical Phenomena in Loop Models
Nahum, Adam.

Critical Phenomena in Loop Models[electronic resource] /by Adam Nahum. - 1st ed. 2015. - XVII, 141 p. 38 illus., 36 illus. in color.online resource. - Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5053. - Springer Theses, Recognizing Outstanding Ph.D. Research,.

Introduction -- Completely Packed Loop Models -- Topological Terms, Quantum Magnets and Deconfined Criticality -- The Statistics of Vortex Lines -- Loop Models with Crossings in 2D -- Polymer Collapse -- Outlook -- Appendix A Potts domain walls and CP^{n-1} -- Appendix B Phases for Hedgehogs & Vortices.

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.

ISBN: 9783319064079

Standard No.: 10.1007/978-3-319-06407-9doiSubjects--Topical Terms:

564049
Physics.

LC Class. No.: QC5.53

Dewey Class. No.: 530.15

Critical Phenomena in Loop Models
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