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Prog. Theor. Phys. Vol. 106 No. 3 (2001) pp. 613-640

CP^N-1 Models with a θ Term and Fixed Point Action

Rudolf Burkhalter,^1,* Masahiro Imachi,^2,** Yasuhiko Shinno^3,*** and Hiroshi Yoneyama^3,****

¹Center for Computational Physics, University of Tsukuba, Tsukuba 305-8577 Japan
²Department of Physics, Yamagata University, Yamagata 990-8560, Japan
³Department of Physics, Saga University, Saga 840-8502, Japan

(Received March 15, 2001)

Abstract:

The topological charge distribution P(Q) is calculated for lattice CP^N-1 models. In order to suppress lattice cutoff effects, we employ a fixed point (FP) action. Through transformation of P(Q), we calculate the free energy F(θ) as a function of the θ parameter. For N=4, scaling behavior is observed for P(Q) and F(θ), as well as the correlation lengths ξ(Q). For N=2, however, scaling behavior is not observed, as expected. For comparison, we also make a calculation for the CP³ model with a standard action. We furthermore pay special attention to the behavior of P(Q) in order to investigate the dynamics of instantons. For this purpose, we carefully consider the behavior of γ _eff, which is an effective power of P(Q) (∼ exp (-CQ^{γ _eff})), and reflects the local behavior of P(Q) as a function of Q. We study γ _eff for two cases, the dilute gas approximation based on the Poisson distribution of instantons and the Debye-Hückel approximation of instanton quarks. In both cases, we find behavior similar to that observed in numerical simulations.

URL : http://ptp.ipap.jp/link?PTP/106/613/
DOI : 10.1143/PTP.106.613

^*E-mail: burkhalt@rccp.tsukuba.ac.jp
^**E-mail: imachi@sci.kj.yamagata-u.ac.jp
^***E-mail: shinno@dirac.phys.saga-u.ac.jp
^****E-mail: yoneyama@cc.saga-u.ac.jp

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Citing Article(s) :

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   Maximum Entropy Method Approach to the θ Term

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3. Progress of Theoretical Physics Vol. 115 No. 5 (2006) pp. 931-949 :

   The Sign Problem and MEM in Lattice Field Theory with the θ Term

   Masahiro Imachi, Yasuhiko Shinno and Hiroshi Yoneyama

4. Progress of Theoretical Physics Vol. 116 No. 1 (2006) pp. 181-196 :

   The θ-Term, CP^N-1 Model and the Inversion Approach in the Imaginary θ Method

   Masahiro Imachi Hitoshi Kambayashi, Yasuhiko Shinno and Hiroshi Yoneyama

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