3D loop models and the CP^{n-1} sigma model

Details 3D loop models and the CP^{n-1} sigma model 3D loop models and the CP^{n-1} sigma model

2011-04-20

arxiv.org/abs/1104.4096v2

Phys.Rev.Lett. 107:110601,2011

Physics

Condensed Matter

Statistical Mechanics

Published version

Scientific paper

10.1103/PhysRevLett.107.110601

Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to $CP^{n-1}$ sigma models, where $n$ is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for $n=1,2,3$, and first order transitions for $n\geq 5$. The results are relevant to line defects in random media, as well as to Anderson localization and $(2+1)$-dimensional quantum magnets.

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