Download Critical Phenomena in Loop Models by Adam Nahum PDF

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 characterize for instance polymer jewelry, or line defects in a lattice magnet, or worldlines of quantum particles.
'Loop versions' 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 homes of line defects in disordered media and to severe phenomena in two-dimensional quantum magnets. the second one half issues two-dimensional loop versions that lie outdoors the normal paradigms: new sorts of serious aspect 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 regarding sigma types on advanced or actual projective area, CP^{n−1} or RP^{n−1} -- on occasion in a 'replica' restrict -- and this thesis is additionally an in-depth research of severe behaviour in those box theories.

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Critical Phenomena in Loop Models

Whilst just about a continuing part 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 debris. 'Loop versions' supply a unifying geometric language for difficulties of this sort.

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A 39, 3221 (2006) A. Mildenberger, F. Evers, Phys. Rev. B 75, 041303 (2007) H. R. Subramaniam, A. A. W. Ludwig, Phys. Rev. W. Lyklema, J. Phys. A. Math. Gen. L. Owczarek, T. Prellberg, J. Stat. Phys. 1 Introduction We begin with a class of three-dimensional loop models that show transitions between two types of phase—one with infinite loops, and one with only short loops. In particular, we focus on a family of completely packed models that may be viewed as discretisations of sigma models with target space CPn−1 (and RPn−1 ).

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