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Prog. Theor. Phys. Vol. 95 No. 1 (1996) pp. 175-189

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Topological Charge Distribution and CP1 Model with θ Term

Ahmed S. Hassan, Masahiro Imachi, Norimasa Tsuzuki and Hiroshi Yoneyama*

Department of Physics, Kyushu University, Fukuoka 812
*Department of Physics, Saga University, Saga 840

(Received October 13, 1995)

Abstract:

The two dimensional CP1 model with a θ term is simulated. We compute the topological charge distribution P(Q) by employing the “set method” and “trial function method”, which are effective in calculations for a very wide range of Q and large volume. The distribiton P(Q) exhibits Gaussian behavior in the small β (inverse coupling constant) region and deviates from this in the large β region. The free energy and its moment are calculated as a function of θ. For small β, the partition function is given by the elliptic theta function, and the distribution of its zeroes on the complex θ plane leads to a first order phase trasition at θ= π. In the large β region, on the other hand, this first order phase transition disappears, but definite conclusion concerning the transition is not reached due to large errors.


URL : http://ptp.ipap.jp/link?PTP/95/175/
DOI : 10.1143/PTP.95.175

[ Full Text PDF : FREE ACCESS (682K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 97 No. 5 (1997) pp. 791-808 :
    Renormalization Group Analysis of U(2) Gauge Theory with θ-Term in 2 Dimensions
    Masahiro Imachi, Takaaki Kakitsuka, Norimasa Tsuzuki and Hiroshi Yoneyama
  2. Progress of Theoretical Physics Vol. 102 No. 3 (1999) pp. 653-670 :
    Two-Dimensional CP2 Model with θ-Term and Topological Charge Distributions
    Masahiro Imachi, Shouhei Kanou and Hiroshi Yoneyama
  3. Progress of Theoretical Physics Vol. 106 No. 3 (2001) pp. 613-640 :
    CPN-1 Models with a θ Term and Fixed Point Action
    Rudolf Burkhalter, Masahiro Imachi, Yasuhiko Shinno and Hiroshi Yoneyama
  4. Progress of Theoretical Physics Vol. 111 No. 3 (2004) pp. 387-411 :
    Maximum Entropy Method Approach to the θ Term
    Masahiro Imachi Yasuhiko Shinno and Hiroshi Yoneyama
  5. 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
  6. Progress of Theoretical Physics Vol. 116 No. 1 (2006) pp. 181-196 :
    The θ-Term, CPN-1 Model and the Inversion Approach in the Imaginary θ Method
    Masahiro Imachi Hitoshi Kambayashi, Yasuhiko Shinno and Hiroshi Yoneyama

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