  We show that Gibbs states of non-homogeneous transverse Ising chains satisfy
a \emph{shielding} property. Namely, whatever the fields on each spin and
exchange couplings between neighboring spins are, if the field in one
particular site is null, the reduced states of the subchains to the right and
to the left of this site are \emph{exactly} the Gibbs states of each subchain
alone. Therefore, even if there is a strong exchange coupling between the
extremal sites of each subchain, the Gibbs states of the each subchain behave
as if there is no interaction between them. In general, if a lattice can be
divided into two disconnected regions separated by an interface of sites with
zero applied field, we can guarantee a similar result only if the surface
contains a single site. Already for an interface with two sites we show an
example where the property does not hold. When it holds, however, we show that
if a perturbation of the Hamiltonian parameters is done in one side of the
lattice, the other side is completely unchanged, with regard to both its
equilibrium state and dynamics.
