264 research outputs found
Exact Analytic Continuation with Respect to the Replica Number in the Discrete Random Energy Model of Finite System Size
An expression for the moment of partition function valid for any finite
system size and complex power 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 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.Comment: 31 pages, 8 eps figure
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