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我们引进了广义Villain公式,考察了双周期紧致U(1)理论的电磁涡旋拓扑结构,得到了该模型在其耦合参数空间中的全部相变结构,其中包括部分禁闭相和二光子相。最后,利用Migdal-Kadanoff重整化群方法的数值结果,得到了这个模型在(N1,N2)=(1,5),(1,6),(1,7)等情况下的相图,从而证实了我们的周期高斯近似下的理论分析。A generalized Villain formula is introduced. In this general Gaussian approximation, the topological properties of the electromagnetic loop for compact QED in four dimensions with an action which is the admixture of two terms with any different periodicities are investigated. The common properties of the phase structure, including two kinds of different partial confinement phases and a two-photon phase, of this model in the whole parameter space are discussed. By using the modified Migdal-Kadanoff group transformation, the phase diagrams for the cases of (N1, N2) = (l,5), (1,6), (1,7) are obtained. The numerical results are consistent with the theoretical analysis.
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