19 FIG. 6: The four observables as a function of µ near the transition between N = 0 and N = 1 at L = 16 and β = 0 . 43 at two different values of L$_{t}$ . The solid lines show the fit of data to the effective quantum mechanics description discussed in the text. 0.292 0.296 0.3 0.304 0 0.2 0.4 0.6 0.8 1 < N > L$_{t}$=960 L$_{t}$=1920 0.292 0.296 0.3 0.304 0 0.05 0.1 0.15 0.2 0.25 < N 2  > - < N > 2 L$_{t}$=960 L$_{t}$=1920 0.292 0.296 0.3 0.304 0 1 2 3 4 L 2 ρ$^{s}$ L$_{t}$=960 L$_{t}$=1920 0.292 0.296 0.3 0.304 0 2000 4000 6000 8000 L$_{t}$=960 L$_{t}$=1920