C. 3D-lattices For these lattices we only have exact data for L = 4 and sampled data for L = 6 , 8 , 12 , 16 , 32 , 64. The situation is actually somewhat better for 3D-lattices. Figure 13 shows some distributions in the vicinity of K ∗ for L = 32 together with the fitted p, q - distributions. For K ≥ K ∗ , just when the distributions become bimodal, the fit is certainly less than perfect, but near K ∗ the p, q -approximation is actually rather good. In the left plot of figure 14 we show z versus log n at K ∗ . The fitted line through the points corresponds to z = − 5 . 3 − log n and is not too bad an approximation. However, in 12 it was estimated that the growth rate exponent at K$_{c}$ of the susceptibility is γ/ν = 1 . 978 ± 0 . 009 (assuming γ = γ ′ and ν = ν ′ ). For the magnetisation it was estimated β/ν = 0 . 5147 ± 0 . 0007. Translated into exponents of n this means 1 . 657 ≤ 1 + γ/ 3 ν ≤ 1 . 663 and 0 . 8282 ≤ 1 − β/ 3 ν ≤ 0 . 8287. If we choose λ$_{1}$ = − 5 / 8 in (108) and (109) the first 41 FIG. 13: Magnetisation distributions for the 32 × 32 × 32-lattice (red) and the fitted P$_{p,q}$ ( n, k ) (blue) vs k − n/ 2 for K = 0 . 2204, K ∗ = 0 . 22066, K = 0 . 2210, K$_{c}$ = 0 . 2216546 and 0 . 2220 (downwards at the y-axis). $^{GLYPH<Minus>}$6000 $^{GLYPH<Minus>}$4000 $^{GLYPH<Minus>}$2000 2000 4000 6000 0.00005 0.00010 0.00015