By Adam Nahum
When with regards to a continual section transition, many actual structures 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 types that lie open air the normal paradigms: new varieties of serious aspect are came across, and new effects given for the common houses of polymer cave in transitions in dimensions.
All of those difficulties are proven to be regarding sigma versions on advanced or genuine projective house, CP^{n−1} or RP^{n−1} -- at times in a 'replica' restrict -- and this thesis can be an in-depth research of severe behaviour in those box theories.
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