Publications [#247613] of Richard G. Palmer
Papers Published
- Van Hemmen, JL; Palmer, RG, The replica method and solvable spin glass model,
Journal of Physics A: General Physics, vol. 12 no. 4
(December, 1979),
pp. 563-580, IOP Publishing, ISSN 0305-4470 [doi]
(last updated on 2024/04/24)Abstract:
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.