04327nam 22008055 450 991030042750332120200702180349.03-319-06407-X10.1007/978-3-319-06407-9(CKB)3710000000251246(EBL)1968533(OCoLC)892749163(SSID)ssj0001372578(PQKBManifestationID)11767966(PQKBTitleCode)TC0001372578(PQKBWorkID)11304693(PQKB)11079119(DE-He213)978-3-319-06407-9(MiAaPQ)EBC1968533(PPN)182100286(EXLCZ)99371000000025124620141001d2015 u| 0engur|n|---|||||txtccrCritical Phenomena in Loop Models /by Adam Nahum1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (150 p.)Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5053Description based upon print version of record.3-319-06406-1 Includes bibliographical references.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.Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5053PhysicsStatistical physicsDynamical systemsMathematical physicsCondensed matterMathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Mathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Condensed Matter Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P25005Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Physics.Statistical physics.Dynamical systems.Mathematical physics.Condensed matter.Mathematical Methods in Physics.Complex Systems.Mathematical Applications in the Physical Sciences.Condensed Matter Physics.Statistical Physics and Dynamical Systems.519530530.15530.41Nahum Adamauthttp://id.loc.gov/vocabulary/relators/aut792263MiAaPQMiAaPQMiAaPQBOOK9910300427503321Critical Phenomena in Loop Models1771529UNINA