随机平面格的对偶分析
Duality analysis on random planar lattice
摘要：
传统的对偶分析是用来确定一个临界点的位置上的一个均匀的晶格没有任何混乱的结构。在本研究中，我们处理的随机平面格，它是由随机结构的基础上的正方形格。我们引入了均匀随机修改的债券稀释和收缩的一部分的单位平方。随机平面晶格包括在控制结构的参数的极端情况下的三角形和六边形晶格。在一个现代的时尚与实空间重整化的对偶分析被发现是可用于估计的随机参数范围宽的临界点的位置。作为一个简单的测试平台，我们证明，我们的方法确实给出了几个临界点的情况下的伊辛和波茨模型，和债券的渗流阈值的随机平面晶格。我们的方法不仅推广了经典统计力学中的对偶分析，而且得到了一类量子纠错码--随机平面晶格上的表面码的最优纠错门限的有趣结果，这种表面码被认为是保护量子态的一种巧妙的技术.
英文摘要：
The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the randomized structure based on the square lattice. We introduce the uniformly random modification by the bond dilution and contraction on a part of the unit square. The random planar lattice includes the triangular and hexagonal lattices in extreme cases of a parameter to control the structure. The duality analysis in a modern fashion with real-space renormalization is found to be available for estimating the location of the critical points with wide range of the randomness parameter. As a simple testbed, we demonstrate that our method indeed gives several critical points for the cases of the Ising and Potts models, and the bond-percolation thresholds on the random planar lattice. Our method leads to not only such an extension of the duality analyses on the classical statistical mechanics but also a fascinating result associated with optimal error thresholds for a class of quantum error correction code, the surface code on the random planar lattice, which known as a skillful technique to protect the quantum state.
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