二维相对论费米子的集团模拟
Cluster simulation of two-dimensional relativistic fermions
摘要：
研究了具有N分量MajoranaWilson费米子场的格点实现中的（离散）Gross-Neveu模型.它除了具有欧几里德晶格对称性之外，还具有内部O（N）对称性。消失质量的离散手征对称性预计只出现在连续极限。晶格理论是第一次重铸方面的二值玻色子链接变量（二聚体）。在这个表示中，它与盖特林格早先借助八顶点模型得到的回路表示相一致，玻尔兹曼权重基本上是正的。虽然标准的局部更新是可能的，在这种形式中，我们构建了一个进一步的精确的转换，我们生成的Peierls轮廓的伊辛模型与当地的行动驻留在plaquettes的二聚体配置。针对该模型，构造了一种Swendsen-Wang型聚类算法。在耦合消失的数值证明，几乎完全消除临界慢化。虽然还需要进一步的测试，一个途径的数值研究的Gross-Neveu模型与前所未有的精度似乎开放。
英文摘要：
The (discrete) Gross-Neveu model is studied in a lattice realization with an N-component Majorana Wilson fermion field. It has an internal O(N) symmetry in addition to the euclidean lattice symmetries. The discrete chiral symmetry for vanishing mass is expected to emerge in the continuum limit only. The lattice theory is first recast in terms of two-valued bosonic link variables (dimers). In this representation, which coincides with the loop representation obtained earlier by Gattringer with the help of eight-vertex-models, the Boltzmann weight is essentially positive. While standard local updates are possible in this form we construct a further exact transformation where we generate dimer configurations as Peierls contours of an Ising model with a local action residing on plaquettes. For this model a Swendsen-Wang type cluster algorithm is constructed. At vanishing coupling it is numerically demonstrated to almost completely eliminate critical slowing down. Although further tests are required, an avenue to numerical studies of the Gross-Neveu model with unprecedented precision seems open.
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