Guo Wenan, Deng Youjin, Blöte Henk W J
Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 1):061112. doi: 10.1103/PhysRevE.79.061112. Epub 2009 Jun 16.
We derive the scaling dimension associated with crossing bonds in the random-cluster representation of the two-dimensional Potts model by means of a mapping on the Coulomb gas. The scaling field associated with crossing bonds appears to be irrelevant on the critical as well as on the tricritical branch. The latter result stands in a remarkable contrast with the existing result for the tricritical O(n) model that crossing bonds are relevant. Although the O(1) model is equivalent with the q=2 random-cluster model, the crossing-bond exponents obtained for these two models appear to be different. We provide an explanation of this peculiar observation. In order to obtain an independent confirmation of the Coulomb gas result for the crossing-bond exponent, we perform a finite-size-scaling analysis based on numerical transfer-matrix calculations.
我们通过在库仑气体上的映射，推导二维Potts模型随机簇表示中与交叉键相关的标度维数。与交叉键相关的标度场在临界分支以及三临界分支上似乎都是无关的。后一结果与三临界O(n)模型中交叉键是相关的现有结果形成了显著对比。尽管O(1)模型与q = 2随机簇模型等价，但这两个模型得到的交叉键指数似乎不同。我们对这一奇特现象给出了解释。为了独立证实库仑气体关于交叉键指数的结果，我们基于数值转移矩阵计算进行了有限尺寸标度分析。
