1979/04/01 by J. Leo van Hemmen, R. G. Palmer · 6 citations
Mathematics · Physics and Astronomy · #Statistical Mechanics and Entropy #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · doi:10.1088/0305-4470/12/4/016
openalex publication_date 1979/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The replica method for random systems is critically examined, with particular emphasis on its application to the Sherrington-Kirkpatrick solution of a 'solvable' spin glass model. The procedure is improved and extended in several ways, including the avoidance of steepest descents and a reformulation which isolates the thermodynamic limit N to infinity . Ideas of analyticity and convexity are employed to investigate the two most dubious steps in the replica method: the extension from an integer number (n) of replicas to real n in the limit n to 0, and the reversal of the limits in n and N. The latter step is proved valid for the Sherrington-Kirkpatrick problem, while the non-uniqueness of the former is held responsible for the unphysical behaviour of the result.