$^{GLYPH<Minus>}$15 $^{GLYPH<Minus>}$10 $^{GLYPH<Minus>}$5 5 10 15 0.02 0.04 0.06 0.08 0.10 0.12 FIG. 6: Magnetisation distributions for C$_{32}$ (points) and fitted P$_{p,q}$ ( n, k ) (lines) vs k − n/ 2 for several temperatures. FIG. 7: Left: y = n ( p − 1) versus K for C$_{n}$ . Right: z = n ( q − 1) versus K for C$_{n}$ . Both plots are for n = 16 , 32 , 64 , 128 (larger cycles stretch farther to the right). 0.2 0.4 0.6 0.8 1.0 1.2 K 0.2 0.4 0.6 0.8 1.0 y 0.2 0.4 0.6 0.8 1.0 1.2 K $^{GLYPH<Minus>}$15 $^{GLYPH<Minus>}$10 $^{GLYPH<Minus>}$5 z at K that gives the maximum value of y . The fitted straight line gives the limit 0 . 1333, very close to 2 / 15. What about the values of y and z ? Indeed they converge beautifully as figure 9 indicates. The limit for y is about 1 . 010 and z approaches a value of − 3 . 537. 36