Download Critical Phenomena in Loop Models by Adam Nahum PDF

By Adam Nahum

When as regards to a continuing part transition, many actual structures can usefully be mapped to ensembles of fluctuating loops, which would signify for instance polymer jewelry, or line defects in a lattice magnet, or worldlines of quantum particles.
'Loop versions' supply 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 homes of line defects in disordered media and to serious phenomena in two-dimensional quantum magnets. the second one half matters two-dimensional loop types that lie open air the traditional paradigms: new varieties of severe aspect are came upon, 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 versions on advanced or actual projective area, CP^{n−1} or RP^{n−1} -- from time to time in a 'replica' restrict -- and this thesis is usually an in-depth research of severe behaviour in those box theories.

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