Spin-glass overlap barriers in three and four dimensions

For the Edwards-Anderson Ising spin-glass model in three and four dimensions $(3d$ and $4d)$ we have performed high statistics Monte Carlo calculations of those free-energy barriers FBq which are visible in the probability density PJ(q) of the Parisi overlap parameter q. The calculations rely on the recently introduced multioverlap algorithm. In both dimensions, within the limits of lattice sizes investigated, these barriers are found to be non-self-averaging and the same is true for the autocorrelation times of our algorithm. Further, we present evidence that barriers hidden in q dominate the canonical autocorrelation times.