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Validation of the Replica Trick for Simple Models

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  • Takashi Shinzato

Abstract

We discuss replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis consists of two analytical techniques, the replica trick (or replica analytic continuation) and the thermodynamical limit (and/or order parameter expansion), we focus our study on replica analytic continuation, which is the mathematical basis of the replica trick. We apply replica analysis to solve a variety of analytical models, and examine the properties of replica analytic continuation. Based on the positive results for these models we propose that replica analytic continuation is a robust procedure in replica analysis.

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  • Takashi Shinzato, 2016. "Validation of the Replica Trick for Simple Models," Papers 1606.07277, arXiv.org.
    • Handle: RePEc:arx:papers:1606.07277
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    File URL: http://arxiv.org/pdf/1606.07277
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