Abstract
We calculate the dynamic local susceptibility χ(ω) of an Ising spin glass near the de Almeida-Thouless (AT) line within the soft spin dynamics for the Sherrington-Kirkpatrick model. We find a crossover from analytic behaviour of χ(ω) at ω=0 above the AT line to a power law behaviour χ(ω)α(−iω) v on the AT line and discuss the analytic properties of the crossover function. The frequencyscale is proportional toθ 1/v , where ρ measures the distance from the AT line. We determine the spectrum of relaxation times which diverge asθ 1−1/v . The average relaxation time diverges asθ −1/v wherev≦1/2. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius χ(ω)−χ(0)α(−iω) v at and below the AT line.
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