By Adam Nahum

ISBN-10: 3319064061

ISBN-13: 9783319064062

ISBN-10: 3319360639

ISBN-13: 9783319360638

When as regards to a continuing section transition, many actual platforms can usefully be mapped to ensembles of fluctuating loops, which would symbolize for instance polymer earrings, or line defects in a lattice magnet, or worldlines of quantum particles.
'Loop types' offer a unifying geometric language for difficulties of this kind.
This thesis goals to increase this language in instructions. the 1st a part of the thesis tackles ensembles of loops in 3 dimensions, and relates them to the statistical houses of line defects in disordered media and to severe phenomena in two-dimensional quantum magnets. the second one half matters two-dimensional loop versions that lie open air the normal paradigms: new forms of serious element are came across, and new effects given for the common homes of polymer cave in transitions in dimensions.
All of those difficulties are proven to be concerning sigma types on complicated or actual projective house, CP^{n−1} or RP^{n−1} -- on occasion in a 'replica' restrict -- and this thesis can also be an in-depth research of serious behaviour in those box theories.

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Critical Phenomena in Loop Models (Springer Theses) by Adam Nahum

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