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Abstract : We study the dynamic fluctuations of the soft-spin version of the Edwards-Anderson model in the critical region for T→Tc+. 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 O1-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 δQαβit1, t2 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 〈δQαβit1, t2δQαβjt3, t4〉ξJ, 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.

Author: Paola Ranieri

Source: https://hal.archives-ouvertes.fr/


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