GENERALIZATION OF THE FORTUIN-KASTELEYN TRANSFORMATION AND ITS APPLICATION TO QUANTUM SPIN SIMULATIONS
GENERALIZATION OF THE FORTUIN-KASTELEYN TRANSFORMATION AND ITS APPLICATION TO QUANTUM SPIN SIMULATIONS
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DOI：
10.1007/bf02178358
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发表时间：
1995-07-01
影响因子：
1.6
通讯作者：
GUBERNATIS, JE
中科院分区：
文献类型：
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作者：
KAWASHIMA, N;GUBERNATIS, JE
我们推广伊辛模型配分函数的 Fortuin-Kasteleyn (FK) 簇表示来表示任意维度上具有任意自旋幅度的量子自旋模型的配分函数。这种广义表示使我们能够开发一种新的集群算法，用于通过世界线蒙特卡罗方法模拟量子自旋系统。由于 Swendsen-Wang 算法是基于 FK 表示的，因此新的聚类算法自然将其作为特例包含在内。除了新表示的一般描述之外，我们还针对一些特殊有趣的情况展示了我们的新算法：伊辛模型、S=1 的反铁磁海森堡模型和一般海森堡模型。新算法适用于任何交换相互作用范围、任何晶格几何形状和任何维度的模型。
We generalize the Fortuin-Kasteleyn (FK) cluster representation of the partition function of the Ising model to represent the partition function of quantum spin models with an arbitrary spin magnitude in arbitrary dimensions. This generalized representation enables us to develop a new cluster algorithm for the simulation of quantum spin systems by the worldline Monte Carlo method. Because the Swendsen-Wang algorithm is based on the FK representation, the new cluster algorithm naturally includes it as a special case. As well as the general description of the new representation, we present an illustration of our new algorithm for some special interesting cases: the Ising model, the antiferromagnetic Heisenberg model with S=1, and a general Heisenberg model. The new algorithm is applicable to models with any range of the exchange interaction, any lattice geometry, and any dimensions.