J L van Hemmen and R G Palmer 1979 J. Phys. A: Math. Gen. 12 563 doi:10.1088/0305-4470/12/4/016
J L van Hemmen and R G Palmer
Show affiliationsThe 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.
75.10.Nr Spin-glass and other random models
02.50.-r Probability theory, stochastic processes, and statistics
Issue 4 (April 1979)
J L van Hemmen and R G Palmer 1979 J. Phys. A: Math. Gen. 12 563
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