Geometrical vs. Fortuin–Kasteleyn clusters in the two-dimensional q-state Potts model
Geometrical vs. Fortuin–Kasteleyn clusters in the two-dimensional q-state Potts model
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DOI：
10.1016/j.nuclphysb.2004.08.030
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发表时间：
2003-11
期刊：
影响因子：
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通讯作者：
W. Janke;A. Schakel
中科院分区：
文献类型：
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作者：
W. Janke;A. Schakel
本文讨论了含空位（0 <$q <$4）的二维q态Potts模型的三临界行为，认为它编码在纯模型的几何自旋团簇的分形结构中.已知的纯模型的临界性质和稀释模型的三临界性质之间的密切联系被证明是反映在Fortuin-Kasteleyn和几何集群之间的密切关系：相同的变换映射到彼此的两个关键制度也映射到彼此的两个集群类型。该图保留了中心电荷，因此两种类型的星团都属于同一普适性类。的几何图片是支持的Monte Carlo模拟的高温表示的伊辛模型（q=2），其中封闭的图形配置生成的大都会更新算法，涉及单个plaquettes。
The tricritical behavior of the two-dimensional q-state Potts model with vacancies for 0⩽q⩽4 is argued to be encoded in the fractal structure of the geometrical spin clusters of the pure model. The known close connection between the critical properties of the pure model and the tricritical properties of the diluted model is shown to be reflected in an intimate relation between Fortuin–Kasteleyn and geometrical clusters: the same transformation mapping the two critical regimes onto each other also maps the two cluster types onto each other. The map conserves the central charge, so that both cluster types are in the same universality class. The geometrical picture is supported by a Monte Carlo simulation of the high-temperature representation of the Ising model (q=2) in which closed graph configurations are generated by means of a Metropolis update algorithm involving single plaquettes.