Loop models with crossings
Loop models with crossings
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DOI：
10.1103/physrevb.87.184204
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发表时间：
2013-05-28
影响因子：
3.7
通讯作者：
Ortuno, M.
中科院分区：
文献类型：
--
作者：
Nahum, Adam;Serna, P.;Ortuno, M.
当允许环路交叉时，二维环路模型的普遍行为会发生显著变化。我们研究模型的交叉分析和广泛的Monte Carlo模拟。我们的主要重点（“完全包装环模型与交叉点”）是一个简单的推广著名的模型，显示了一个有趣的相图连续相变的一种新的。这些分离的不寻常的“戈德斯通”阶段观察到以前的阶段与短循环。利用到Z（2）格点规范理论的映射，我们证明了该模型的连续描述是sigma模型在真实的射影空间（RPn-1）上的一个复制极限.这个场论支持Z（2）点缺陷，它在转变处增殖。除了研究新的临界点，我们详细描述了戈德斯通相的普适性质，比较重整化群（RG）计算与数值数据的线性大小的系统L = 10（6）在循环逸度n = 1。(Very由于相关函数的对数形式和其它可观测量，需要大尺寸。该模型是相关的聚合物的崩溃的边缘，在参数空间中的一个特定的点映射到自避免的痕迹在他们的θ点，我们使用RG处理的扰动西格玛模型来解决一些令人困惑的功能在以前的文献中的痕迹。最后，这里考虑的相变之一是无序电子系统中的那些相变的密切类似物，特别是安德森金属-绝缘体转变，并提供了一个更简单的背景下，研究这些知之甚少（中心电荷零）的临界点的属性。
The universal behavior of two-dimensional loop models can change dramatically when loops are allowed to cross. We study models with crossings both analytically and with extensive Monte Carlo simulations. Our main focus (the "completely packed loop model with crossings") is a simple generalization of well-known models that shows an interesting phase diagram with continuous phase transitions of a new kind. These separate the unusual "Goldstone" phase observed previously from phases with short loops. Using mappings to Z(2) lattice gauge theory, we show that the continuum description of the model is a replica limit of the sigma model on real projective space (RPn-1). This field theory sustains Z(2) point defects, which proliferate at the transition. In addition to studying the new critical points, we characterize the universal properties of the Goldstone phase in detail, comparing renormalization group (RG) calculations with numerical data on systems of linear size up to L = 10(6) at loop fugacity n = 1. (Very large sizes are necessary because of the logarithmic form of correlation functions and other observables.) The model is relevant to polymers on the verge of collapse, and a particular point in parameter space maps to self-avoiding trails at their Theta point; we use the RG treatment of a perturbed sigma model to resolve some perplexing features in the previous literature on trails. Finally, one of the phase transitions considered here is a close analog of those in disordered electronic systems-specifically, Anderson metal-insulator transitions-and provides a simpler context in which to study the properties of these poorly understood (central-charge-zero) critical points.