Spatial correlation functions in three-dimensional Ising spin glasses

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