Absolute continuity between a Gibbs measure and its translate

We look for an overestimation of the distance in total variation between a Gibbs measure on $R^{Z^d}$ and its translate by a vector of this space. This can be done thanks to a control of the interdependence between the spins at distinct sites, i.e., prescribing some restrictions for the associated potential. We can then conclude, for precise cases, with the equivalence of the initial measure and its translate.