2016/06/23 by Shinzato, Takashi
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Physical sciences #Information Theory (cs.IT) #Portfolio Management (q-fin.PM) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1606.07277
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.