The $θ$-term, CP$^{N-1}$ Model and the Inversion Approach in the Imaginary $θ$ Method

Details The $θ$-term, CP$^{N-1}$ Model and the Inversion Approach in the Imaginary $θ$ Method The $θ$-term, CP$^{N-1}$ Model and the Inversion Approach in the Imaginary $θ$ Method

2006-01-23

arxiv.org/abs/hep-lat/0601028v4

Physics

High Energy Physics

High Energy Physics - Lattice

PTPTEX<ver.0.9>, 17 pages with 13 figures. Some sentences were corrected

Scientific paper

10.1143/PTP.116.181

The weak coupling region of CP$^{N-1}$ lattice field theory with the $\theta$-term is investigated. Both the usual real theta method and the imaginary theta method are studied. The latter was first proposed by Bhanot and David. Azcoiti et al. proposed an inversion approach based on the imaginary theta method. The role of the inversion approach is investigated in this paper. A wide range of values of $h=-{\rm Im} \theta$ is studied, where $\theta $ denotes the magnitude of the topological term. Step-like behavior in the $x$-$h$ relation (where $x=Q/V$, $Q$ is the topological charge, and $V$ is the two dimensional volume) is found in the weak coupling region. The physical meaning of the position of the step-like behavior is discussed. The inversion approach is applied to weak coupling regions.

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