LEADER 04327nam 22008055 450 001 9910300427503321 005 20200702180349.0 010 $a3-319-06407-X 024 7 $a10.1007/978-3-319-06407-9 035 $a(CKB)3710000000251246 035 $a(EBL)1968533 035 $a(OCoLC)892749163 035 $a(SSID)ssj0001372578 035 $a(PQKBManifestationID)11767966 035 $a(PQKBTitleCode)TC0001372578 035 $a(PQKBWorkID)11304693 035 $a(PQKB)11079119 035 $a(DE-He213)978-3-319-06407-9 035 $a(MiAaPQ)EBC1968533 035 $a(PPN)182100286 035 $a(EXLCZ)993710000000251246 100 $a20141001d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCritical Phenomena in Loop Models /$fby Adam Nahum 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (150 p.) 225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053 300 $aDescription based upon print version of record. 311 $a3-319-06406-1 320 $aIncludes bibliographical references. 327 $aIntroduction -- 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. 330 $aWhen close to a continuous phase transition, many physical systems can usefully be mapped to ensembles of fluctuating loops, which might represent for example polymer rings, or line defects in a lattice magnet, or worldlines of quantum particles. 'Loop models' provide a unifying geometric language for problems of this kind. This thesis aims to extend this language in two directions. The first part of the thesis tackles ensembles of loops in three dimensions, and relates them to the statistical properties of line defects in disordered media and to critical phenomena in two-dimensional quantum magnets. The second part concerns two-dimensional loop models that lie outside the standard paradigms: new types of critical point are found, and new results given for the universal properties of polymer collapse transitions in two dimensions. All of these problems are shown to be related to sigma models on complex or real projective space, CP^{n?1} or RP^{n?1} -- in some cases in a 'replica' limit -- and this thesis is also an in-depth investigation of critical behaviour in these field theories. 410 0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053 606 $aPhysics 606 $aStatistical physics 606 $aDynamical systems 606 $aMathematical physics 606 $aCondensed matter 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aCondensed Matter Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25005 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aPhysics. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 0$aMathematical physics. 615 0$aCondensed matter. 615 14$aMathematical Methods in Physics. 615 24$aComplex Systems. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aCondensed Matter Physics. 615 24$aStatistical Physics and Dynamical Systems. 676 $a519 676 $a530 676 $a530.15 676 $a530.41 700 $aNahum$b Adam$4aut$4http://id.loc.gov/vocabulary/relators/aut$0792263 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300427503321 996 $aCritical Phenomena in Loop Models$91771529 997 $aUNINA