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Progress of Theoretical Physics
Vol. 111 No. 5 (2004) pp. 661-688
URL : http://ptp.ipap.jp/link?PTP/111/661/
DOI : 10.1143/PTP.111.661

Exact Analytic Continuation with Respect to the Replica Number in the Discrete Random Energy Model of Finite System Size

Kenzo Ogure1,* and Yoshiyuki Kabashima2,**

1Theory Group, Institute for Cosmic Ray Research, Kashiwa 277-8582, Japan
2Department of Computational Intelligence and Systems Science,
Tokyo Institute of Technology, Yokohama 226-8502, Japan

(Received October 21, 2003)

An expression for the moment of the partition function valid for any finite system size N and complex power n [\Re(n) > 0] is obtained for a simple spin glass model termed the discrete random energy model (DREM). We investigate the behavior of this moment in the thermodynamic limit, N →∞, using this expression, and we find that a phase transition occurs at a certain real value of the replica number when the temperature is sufficiently low. This represents a direct clarification of the scenario of replica symmetry breaking of the DREM in the replica number space without use of the replica trick. The validity of the expression is confirmed numerically.


*E-mail: ogure@icrr.u-tokyo.ac.jp
**E-mail: kaba@dis.titech.ac.jp


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Citing Article(s) :

  1. Journal of the Physical Society of Japan 74 (2005) pp. 488-497 :
    Statistical Mechanical Approach to Error Exponents of Lossy Data Compression
    Tadaaki Hosaka and Yoshiyuki Kabashima
  2. Journal of the Physical Society of Japan 77 (2008) 074718 (6 pages) :
    Large Deviation Property of Free Energy in p-Body Sherrington–Kirkpatrick Model
    Tetsuya Nakajima and Koji Hukushima
  3. Progress of Theoretical Physics Supplement No.157 (2005) pp. 103-106 :
    An Exact Analytic Continuation to Complex Replica Number in the Discrete Random Energy Model of Finite System Size
    Kenzo Ogure and Yoshiyuki Kabashima

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