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Analogous ly, the second cumulant (normalised) should behave as 

<img src='content_image/360989.jpg'>

where the ϱ$_{m}$ were defined in section VIII. Note that for a fixed z the ϱ$_{m}$ now depend only on a . The third and fourth cumulants of the absolute magnetisation, divided by respectively 8 n 9 / 4 and 16 n $^{3}$, quite analogously approach their corresponding limits 

and 

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Through a simple scaling analysis based on our sampled data we have found that the nor- malised third cumulant has a limit maximum of about 0 . 0205 and a minimum of − 0 . 0500. The fourth normalised cumulant has a limit maximum of 0 . 0229 and a minimum of − 0 . 0278, based upon our sampled data. Choosing z = − 9 . 87 puts the maximums and minimums of the limit curves at appropriate values. Now we identify the coupling K where the minimum of the fourth cumulant occurs with the point a where the minimum of the corresponding limit curve occurs and likewise for the maximum, thus providing us with a rescaling trans- lating K into a . In figure 22 and 23 the first four cumulants are shown together with their estimated limit curves for z = − 9 . 87. Indeed the red curve may provide us with a limit. 

Given a lattice size L we denote by K$_{min}$ ( L ) the location of the minimum fourth cumulant and by K$_{max}$ ( L ) the location of the maximum. Analogously for the limit curve, given a z we 

