3D loop models and the CP(n-1) sigma model.
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≥5. The results are relevant to line defects in random media, as well as to Anderson localization and (2+1)-dimensional quantum magnets.
Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
Adam
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Nahum
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Chalker
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Serna
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Ortuño
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Somoza