The effect of specific ionic interactions on the Debye length has been studied using a simple model Hamiltonian for a binary mixture of anions and cations in the framework of the field theory. The Hamiltonian contains the Coulombic interaction and an independent non-Coulombic part describing a binary mixture of equivalent uncharged particles. We use a local and quadratic approximation to calculate the partition function via a functional integral. The Debye limiting law is obtained with a renormalized screening length. The screening is enhanced when the specific interactions favor demixion. This is illustrated on the example of an asymmetric hard sphere mixture.