The results on criticality can be expressed in another way which links with catastrophe theory. First, let us return to the situation where we are considering the variation of possible equilibrium values with k in the a > 1 case. In Figure 5.11 the point W~, when it exists, and the origin, are the stable equilibrium points. We can plot the values of these against a varying k val ue. This is done in Fi gure 5.16. This curve is imlTEdiately reminiscent of the fold catastrophe, but with zero states added. We could also then do corresponding plots for a and 8 and this is done in Fi gures 5.17 and 5.18. In each case, they assulTE that k and the other pararreters are fixed. The
basis of these plots can be worked out by adding a k-line in Figures 5.12 and 5.13 in turn and examining the variation in W~
J against the corresponding parameter.