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

Kenzo Ogure; Yoshiyuki Kabashima

doi:10.1143/ptp.111.661

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

Kenzo Ogure·Yoshiyuki Kabashima

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Abstract

An expression for the moment of 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 {\em discrete random energy model} (DREM). We investigate the behavior of the moment in the thermodynamic limit $N \to \infty$ using this expression, and find that a phase transition occurs at a certain real replica number when the temperature is sufficiently low, directly clarifying the scenario of replica symmetry breaking of DREM in the replica number space {\em without using the replica trick}. The validity of the expression is numerically confirmed.

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Kenzo Ogure, Yoshiyuki Kabashima. 2004-03-22. Exact Analytic Continuation with Respect to the Replica Number in the Discrete Random Energy Model of Finite System Size. https://doi.org/10.1143/ptp.111.661

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