ω = 0 α = 1 / 2 α = 0 α = 0 . 4 α = 0 . 6 α = 0 . 7 ω = 0 . 2 ω = 0 . 5 ω = 1 $_{/}$√$_{2}$ ω = 1 λ (2) c = 2 λ (2) c = 1 λ (2) c = 0 . 5 λ (2) c = 0 . 25 λ (2) c = 0 . 83 λ (2) c = 1 . 01 λ (2) c = 1 . 17 λ (2) c = 1 . 45 TABLE I: Critical couplings λ (2) c for the eight cases depicted in Fig. 6 -0.8 -0.6 -0.4 -0.2  0  2  2.5  3  3.5  4 log 10  r max  ( (2) c ) log$_{10}$ N -1.0 -0.8 -0.6  2  2.5  3  3.5  4 log 10  r max  ($^{λ}$ (2) c ) log$_{10}$ N (a) ω = 0 (b) α = 1 / 2 FIG. 7: r$_{max}$ ( λ (2) c ) in function of the size of the environment N , in a double logarithmic scale. Left panel represents ω = 0; right panel α = 1 / 2. Squares represent the case α = 0 (left) and ω = 0 . 2 (right); circles, α = 0 . 4 (left) and ω = 0 . 5 (right); upper triangles, α = 0 . 6 (left) and ω = 1 $_{/}$√$_{2}$ (right); lower triangles, α = 0 . 7 (left) and ω = 1 (right). Straight lines represent the best fit to a power law r$_{max}$ ( λ (2) c ) = AN − $^{γ}$. beyond this value is very difficult since for a complete calculation of r$_{max}$ ( λ (2) c ) all the eigen- values and eigenvectors of the environmental Hamiltonian are needed. Starting with systems of N = 100, we analize the finite size scaling along two orders of magnitude. In Fig. 7 we show how r$_{max}$ ( λ (2) c ) evolves with the size N of the environment, both for ω = 0 and several values of α (left panel), and α = 1 / 2 and several values of ω = 0. In all the cases, a power-law scaling r$_{max}$ ( λ (2) c ) ∼ N − γ is observed, and therefore we can expect that r$_{max}$ ( λ (2) c ) → 0 in the thermodynamical limit N → ∞ . Nevertheless, subtle differences between verying α with ω = 0 and varying ω with α = 1 / 2 are observed. The results for the exponent γ , shown in Tab. II, are very close to the proposed γ = 1 / 4 [9] for ω = 0. 20