Deviations from Scaling



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Deviations from Scaling

One simple feature of (8) is that, when is plotted against , the curves for different intersect at a common point . In practice the data do not behave in exactly this way. There is a small deviation from scaling. This deviation could be taken into account by adding an extra term to (8) which depends on but not on . Consider, however, the form

 

which represents the most general form of such a correction. If a specific form for the correction were assumed it would require at least 4 independent fitting parameters to represent , including and , and may still not represent the true deviation from scaling. It seems better therefore to fit an independent for each value of and therefore to make no assumption about the nature of the deviation from scaling, other than that it is non-critical, and therefore independent of , in the region of interest. By fitting the data to (10) in this way the exponent is derived solely from the gradient of vs. and the intercept is allowed to float. The results of such fits are shown in figure 1.

 



Angus MacKinnon - Aonghas Mac Fhionghuin
Tue Nov 29 13:32:02 gmt 1994