Linking numbers for self-avoiding loops and percolation: application to the spin quantum hall transition
Linking numbers for self-avoiding loops and percolation: application to the spin quantum hall transition
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自回避环和渗透的链接数：在自旋量子霍尔跃迁中的应用
DOI：
10.1103/physrevlett.84.3507
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发表时间：
1999
影响因子：
8.6
通讯作者：
J. Cardy
中科院分区：
文献类型：
--
作者：
J. Cardy
在二维O（n）和Q-态Potts模型中引入非定域扭曲算子，计算围绕给定点的自避免环（分别为渗流簇）的数目.它们的尺度尺寸是精确计算的。这会产生许多结果：例如，为了将一个给定的点连接到一个无限远的边界，必须穿过的渗透簇的数量。其平均值表现为（1/3sqrt[3] pi）|ln（p（c）-p）|如p-->p（c）-。作为应用，我们计算了自旋霍尔跃迁处电导率的精确值sqrt[3]/2，以及具有两个扩展边缘接触的任意单连通几何中平均电导的形状依赖性。
Nonlocal twist operators are introduced for the O(n) and Q-state Potts models in two dimensions which count the numbers of self-avoiding loops (respectively, percolation clusters) surrounding a given point. Their scaling dimensions are computed exactly. This yields many results: for example, the number of percolation clusters which must be crossed to connect a given point to an infinitely distant boundary. Its mean behaves as (1/3sqrt[3] pi) |ln( p(c)-p)| as p-->p(c)-. As an application we compute the exact value sqrt[3]/2 for the conductivity at the spin Hall transition, as well as the shape dependence of the mean conductance in an arbitrary simply connected geometry with two extended edge contacts.