FIG. 7: The four observables as a function of µ near the transition between N = 0 and N = 1 at L = 6 and β = 0 . 2 for L$_{t}$ = 540 and 1080 . The solid lines show the fit of data to the effective quantum m echanics description discussed in the text. 1.852 1.856 1.86 1.864 0 0.2 0.4 0.6 0.8 1 < N > L$_{t}$=540 L$_{t}$=1080 0 0.05 0.1 0.15 0.2 0.25 < N 2 > - < N > 2 L$_{t}$=540 L$_{t}$=1080 1.852 1.856 1.86 1.864 0 0.1 0.2 0.3 L 2 ρ$^{s}$ L$_{t}$=540 L$_{t}$=1080 1.852 1.856 1.86 1.864 250 500 750 1000 L$_{t}$=540 L$_{t}$=1080 20