Dynamic Fluctuations in a Short-range Spin Glass Model

(Received 18 May 1995, revised 11 October 1995, accepted 29 February 1996)

Abstract
We study the dynamic fluctuations of the soft-spin version of the Edwards-Anderson model in the critical region for . First we solve the infinite-range limit of the model using the random matrix method. We define the static and dynamic 2-point and 4-point correlation functions at the order O(1/N) and we verify that the static limit obtained from the dynamic expressions is correct. In a second part we use the functional integral formalism to define an effective short-range Lagrangian L for the fields up to the cubic order in the series expansion around the dynamic Mean-Field value . We find the more general expression for the time depending non-local fluctuations, the propagators , in the quadratic approximation. Finally we compare the long-range limit of the correlations, derived in this formalism, with the correlations of the infinite-range model studied with the previous approach (random matrices).