Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
Phys Rev Lett. 2011 Sep 9;107(11):110601. doi: 10.1103/PhysRevLett.107.110601. Epub 2011 Sep 8.
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.
许多统计力学问题都可以用随机曲线来描述；我们考虑了一类三维环模型，它们是这种集合的原型。这些模型表现出具有无限环和短环相的相变。我们将它们映射到 CP(n-1) sigma 模型，其中 n 是环逸度。通过蒙特卡罗模拟，我们发现 n=1、2、3 时有连续相变，n≥5 时有一级相变。这些结果与随机介质中的线缺陷以及安德森局域化和(2+1)维量子磁体有关。
