The replica method and solvable spin glass model

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Van Hemmen, JL; Palmer, RG

Published Date

  • December 1, 1979

Published In

Volume / Issue

  • 12 / 4

Start / End Page

  • 563 - 580

International Standard Serial Number (ISSN)

  • 0305-4470

Digital Object Identifier (DOI)

  • 10.1088/0305-4470/12/4/016

Citation Source

  • Scopus