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We solve a random energy model with complex replica number and complex temperature values, and discuss the ensuing phase structure. A connection with string models and their phase structure is analyzed from the REM point of view. The REM analysis yields a few integer dimensions as special points of the REM phase diagram. For N = 1 superstrings, there is a distinguished dimension 5.
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David B. Saakian (2009) studied this question.
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