and L$_{t}$ is sufficiently large. The corresponding effective paramet ers are tabulated in Tabs. II, III and IV. The fits always give reasonable χ $^{2}$/DOF , which are shown in the last four columns, one for each observable. We note that as β becomes smaller, µ (0) c becomes larger while µ (1) c − µ (0) c becomes smaller. This is the reason it becomes difficult to ma tch the data to an effective quantum mechanics description at small β without going to very large L$_{t}$ . Note also that the value of µ (0) c has approximately reached the thermodynamic limit at β = 0 . 2 for L = 8 . We plot our four observables near µ (0) c at L = 16 and β = 0 . 43 in Fig. 6 and at L = 6 and β = 0 . 2 in Fig. 7 along with the fits. 13 TABLE I: Parameters of effective quantum mechanics that describes the data for the L = 2 lattice at β = 0 . 43 . N µ ( N ) c ρ$_{0}$ ρ$_{1}$ χ$_{0}$ χ $^{2}$/DOF β = 0 . 43 0 0.82444(3) 0.2114(2) 0.2713(2) 2.349(4) 1.23 1.43 0.70 0.58 1 1.22462(2) 0.2715(2) 0.2983(2) 2.817(4) 0.52 0.50 1.04 0.81 2 1.51567(2) 0.298(1) 0.312(1) 3.013(4) 0.73 0.70 1.20 1.28 3 1.74436(2) 0.313(1) 0.321(1) 3.121(4) 1.02 1.02 0.78 1.14 β = 0 . 50 0 0.63275(3) 0.288(1) 0.336(1) 2.63(1) 0.58 0.56 1.33 0.68 1 1.05865(2) 0.339(1) 0.362(1) 2.957(9) 0.72 0.69 0.71 1.47 2 1.35787(2) 0.364(1) 0.376(1) 3.116(8) 0.89 0.85 1.37 0.94 3 1.58951(2) 0.377(1) 0.386(1) 3.212(8) 0.57 0.54 1.07 1.00 β = 0 . 20 0 1.9141(1) 0.0414(2) 0.0884(2) 1.458(9) 0.55 0.52 0.47 0.81 1 2.12263(9) 0.0884(2) 0.1106(3) 2.14(1) 0.41 0.40 1.38 0.98 2 2.33075(8) 0.1109(2) 0.1178(3) 2.40(1) 0.43 0.34 1.02 1.67 3 2.52196(8) 0.1186(3) 0.1150(2) 2.48(1) 0.56 0.52 1.36 1.17