J. Phys. I France
Volume 6, Number 6, June 1996
Page(s) 807 - 822
DOI: 10.1051/jp1:1996243
J. Phys. I France 6 (1996) 807-822

Dynamic Fluctuations in a Short-range Spin Glass Model

Paola Ranieri

Dipartimento di Fisica, Università di Roma La Sapienza, P. Aldo Moro 2, 00185 Roma, Italy

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

We study the dynamic fluctuations of the soft-spin version of the Edwards-Anderson model in the critical region for $T\rightarrow T_{\rm c}^+$. 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 $\delta Q^{\alpha \beta}_{i}(t_{1}, t_{2})$ up to the cubic order in the series expansion around the dynamic Mean-Field value $\overline{Q^{\alpha \beta}}(t_{1}, t_{2})$. We find the more general expression for the time depending non-local fluctuations, the propagators $[\langle \delta Q^{\alpha \beta}_{i}(t_{1}, t_{2})\delta Q^{\alpha \beta}_{j}(t_{3}, t_{4})\rangle_\xi ]J$, 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).

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