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

Journal article

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.

Authors: Nahum, A; Chalker, J; Serna, P; Ortuño, M; Somoza, A

• Journal: Phys.Rev.Lett.
• Volume: 107
• Issue: 11
• Pages: 110601
• Publication date: 2011-04-20
• DOI: 10.1103/PhysRevLett.107.110601
• EISSN: 1079-7114
• ISSN: 0031-9007
• Language: English
• Keywords: cond-mat.dis-nn; cond-mat.stat-mech