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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. 

