Asymptotic self-similarity group

The curves of Figure 5.14 show how the values of the fixed point a (r) and the anomalous dimension /1(t) depend on the choice of scale. Both a (r) and A(t) decrease monotonically as the value of the scale increases. To determine the proper threshold value t, in excess of which the propagator amplitude is self-similar for all values of the group parameter t, we must acquire independent information about the expected asymptotic behavior of the effective coupling function such as, for example, the correct limiting value (at t oo) of the coupling function. One possibility is that the onset of self-similarity will become apparent if one selects a sufficiently large value of the scale. Implementation of this notion requires an extrapolation of our calculated results to infinite values of t, a procedure that leads to the results (t oo) 0.95 and X(z co) 0.12. 

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