$^{GLYPH<Minus>}$4000 $^{GLYPH<Minus>}$2000 2000 4000 0.00005 0.00010 0.00015 0.00020 0.00025 0.00030 FIG. 16: Magnetisation distributions for the 12 × 12 × 12 × 12-lattice (red) and the fitted P$_{p,q}$ ( n, k ) (blue) vs k − n/ 2 for K = 0 . 1490, K ∗ = 0 . 149255, K$_{c}$ = 0 . 149695, K = 0 . 1500 and K = 0 . 1505 (downwards at the y-axis). could be incorrect or our data could be suffering from very slow convergence. In the right plot of figure 17 we show y versus z for K > K ∗ together with the curve y = 2 w with w defined by (59). In figure 18 we show y and z versus K for K > K ∗ . The red line is located at K$_{c}$ ≈ 0 . 1496497, estimated in $^{22}$. For the 5-dimensional lattices we have sampled data of magnetisation distributions only for L = 4 , 6 , 8 , 10 , 12. The distributions in figure 19 are extremely well fitted by p, q -binomial distributions; it is almost impossible to tell them apart with the naked eye. In five dimensions the susceptibility near K$_{c}$ scales as L 5 / $^{2}$, see$^{23}$. Thus σ$_{2}$ should scale as n 3 / 2 which is exactly what we receive when keeping z fixed. So, for z constant we obtain σ$_{1}$ ∝ n 3 / 4 and σ$_{2}$ ∝ n 3 / $^{2}$. The left plot of figure 20 shows z at K ∗ for L = 4 , 6 , 8 , 10 , 12. If z approaches a constant E. 5D-lattices 44