Dynamic scaling for spin glasses near the de Almeida-Thouless line

We calculate the dynamic local susceptibility () 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 () at =0 above the AT line to a power law behaviour ()(–i)^v on the AT line and discuss the analytic properties of the crossover function. The frequencyscale is proportional to^1/v, where measures the distance from the AT line. We determine the spectrum of relaxation times which diverge as^1–1/v. The average relaxation time diverges as^–1/v wherev1/2. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius ()–(0)(–i)^v at and below the AT line.