We study a hierarchical disordered pinning model with site disorder for
which, like in the bond disordered case [6, 9], there exists a value of a
parameter b (enters in the definition of the hierarchical lattice) that
separates an irrelevant disorder regime and a relevant disorder regime. We show
that for such a value of b the critical point of the disordered system is
different from the critical point of the annealed version of the model. The
proof goes beyond the technique used in [9] and it takes explicitly advantage
of the inhomogeneous character of the Green function of the model.Comment: 13 pages, 1 figure, final version accepted for publication. to appear
in Probability Theory and Related Field