Spatial correlation functions in three-dimensional Ising spin glasses

We investigate spin-spin correlation functions in the low-temperature phase of spin-glasses. Using the replica field theory formalism, we examine in detail their infrared long-distance behavior. In particular we identify a longitudinal mode that behaves as massive at intermediate-length scales near-infrared region. These issues are then addressed by numerical simulation; the analysis of our data is compatible with the prediction that the longitudinal mode appears as massive, i.e., that it undergoes an exponential decay, for distances smaller than an appropriate correlation length.