Publications [#247613] of Richard G. Palmer

Papers Published
  1. Hemmen, JLV; Palmer, RG, The replica method and solvable spin glass model, Journal of Physics A: Mathematical and General, vol. 12 no. 4 (1979), pp. 563-580 [doi] .

    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.