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Geometric symmetries and cluster simulations

机译：几何对称性和聚类模拟

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Cluster Monte Carlo methods are especially useful for applications in the vicinity of phase transitions, because they suppress critical slowing down; this may reduce the required simulation times by orders of magnitude. In general, the way in which cluster methods work can be explained in terms of global symmetry properties of the simulated model. In the case of the Swendsen-Wang and related algorithms for the Ising model, this symmetry is the plus-minus spin symmetry; therefore, these methods are not directly applicable in the presence of a magnetic field. More generally, in the case of the Potts model, the Swendsen-Wang algorithm relies on the permutation symmetry of the Potts states. However, other symmetry properties can also be employed for the formulation of cluster algorithms. Besides of the spin symmetries, one can use geometric symmetries of the lattice carrying the spins. Thus, new cluster simulation methods are realized for a number of models. This geometric method enables the investigation of models that have thus far remained outside the reach of cluster algorithms. Here, we present some simulation results for lattice gases, and for an Ising model at constant magnetization. This cluster method is also applicable to the Blume-Capel model, including its tricritical point. (C) 1998 Elsevier Science B.V. All rights reserved. [References: 12]
机译：群集蒙特卡洛方法在相变附近的应用中特别有用，因为它们可以抑制临界减慢。这样可以将所需的仿真时间减少几个数量级。通常，可以根据模拟模型的全局对称特性来解释聚类方法的工作方式。对于Ising模型的Swendsen-Wang和相关算法，此对称性为正负自旋对称性;因此，这些方法不适用于存在磁场的情况。更一般而言，在Potts模型的情况下，Swendsen-Wang算法依赖于Potts状态的排列对称性。但是，其他对称属性也可以用于聚类算法的制定。除了自旋对称性之外，还可以使用承载自旋的晶格的几何对称性。因此，针对许多模型实现了新的集群仿真方法。这种几何方法使得能够研究迄今仍不属于聚类算法的模型。在这里，我们给出了晶格气体和恒定磁化强度下的伊辛模型的一些模拟结果。此聚类方法也适用于Blume-Capel模型，包括其三临界点。 （C）1998 Elsevier Science B.V.保留所有权利。 [参考：12]

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