2010/10/19 by Victor Dotsenko, Dotsenko, Victor
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Scientific Research and Discoveries #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1010.3913
13 pages, 3 figures
arxiv created 2010/10/19 · openalex publication_date 2010/10/19 · arxiv updated 2010/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A systematic replica field theory calculations are analysed using the examples of two particular one-dimensional "toy" random models with Gaussian disorder. Due to apparent simplicity of the model the replica trick calculations can be followed here step by step from the very beginning till the very end. In this way it can be easily demonstrated that formally at certain stage of the calculations the implementation of the standard replica program is just impossible. On the other hand, following the usual "doublethink" traditions of the replica calculations (i.e. closing eyes on the fact that certain suggestions used in the calculations contradict to each other) one can easily fulfil the programme till the very end to obtain physically sensible result for the entire free energy distribution function.