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- W1564062570 abstract "We consider the statistical mechanics of a class of models involving close-packed loops with fugacity $n$ on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretizations of $C{P}^{nensuremath{-}1}$ $ensuremath{sigma}$ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the $ensuremath{sigma}$ model, and we discuss the relationship between loop properties and $ensuremath{sigma}$ model correlators. On large scales, loops are Brownian in an ordered phase and have a nontrivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for $n=1,2,3$ and first order transitions for $nensuremath{ge}4$. We also give a renormalization-group treatment of the $C{P}^{nensuremath{-}1}$ model that shows how a continuous transition can survive for values of $n$ larger than (but close to) 2, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including $mathrm{SU}(n)$ quantum magnets in (2+1) dimensions, Anderson localization in symmetry class $C$, and the statistics of random curves in three dimensions." @default.
- W1564062570 created "2016-06-24" @default.
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- W1564062570 date "2013-10-11" @default.
- W1564062570 modified "2023-10-18" @default.
- W1564062570 title "Phase transitions in three-dimensional loop models and the<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>C</mml:mi><mml:msup><mml:mi>P</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>sigma model" @default.
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- W1564062570 doi "https://doi.org/10.1103/physrevb.88.134411" @default.
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