2011/04/30 by Adam Nahum, J. T. Chalker, Pablo Serna +3 · 73 citations
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Computer science #Distributed and Parallel Computing Systems #Quantum chaos and dynamical systems #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.107.110601
published in Physical Review Letters 107(11), 110601 (American Physical Society) · Published version
openalex publication_date 2011/09/08 · arxiv created 2011/09/20 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.