The replica method and solvable spin glass model
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.
Duke Scholars
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- Mathematical Physics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Mathematical Physics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences