Validation of the replica trick for simple models. (26th April 2018)

• Record Type: Journal Article
• Authors: Shinzato, Takashi
• Is Part Of: Journal of statistical mechanics. (2018:Apr.)
• Publication Date: 2018-04-26
• Subjects: 7; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aab686
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We discuss the replica analytic continuation using several simple models in order to prove mathematically the validity of the 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.