  We present results of a Monte Carlo study of the equilibrium dynamics of the
one dimensional long-range Ising spin glass model. By tuning a parameter
$\sigma$, this model interpolates between the mean field
Sherrington-Kirkpatrick model and a proxy of the finite dimensional
Edward-Anderson model. Activated scaling fits for the behavior of the
relaxation time $\tau$ as a function of the number of spins $N$ (Namely
$\ln(\tau)\propto N^{\psi}$) give values of $\psi$ that are not stable against
inclusion of subleading corrections. Critical scaling ($\tau\propto N^{\rho}$)
gives more stable fits, at least in the non mean field region. We also present
results on the scaling of the time decay of the critical remanent magnetization
of the Sherrington-Kirkpatrick model, a case where the simulation can be done
with quite large systems and that shows the difficulties in obtaining precise
values for dynamical exponents in spin glass models.
