  We study the discrete massless Gaussian Free Field on Z^d, d \geq 2, in the
presence of a disordered square-well potential supported on a finite strip
around zero. The disorder is introduced by reward/penalty interaction
coefficients, which are given by i.i.d. random variables. In the previous note,
we proved under minimal assumptions on the law of the environment, that the
quenched free energy associated to this model exists in R^+, is deterministic,
and strictly smaller than the annealed free energy whenever the latter is
strictly positive. Here we consider Bernoulli reward/penalty coefficients b e_x
+ h with P(e_x=-1)=P(e_x=+1)=1/2 for all x in Z^d, and b > 0, h in R. We prove
that in the plane (b,h), the quenched critical line (separating the phases of
positive and zero free energy) lies strictly below the line h = 0, showing in
particular that there exists a non trivial region where the field is localized
though repulsed on average by the environment.
