The effective exponent gamma(Q) and the slope of the beta function
  The slope of the beta function at a fixed point is commonly thought to be RG invariant and to be the critical exponent gamma* that governs the approach of any physical quantity R to its fixed-point limit: R*-R proportional to Q^gamma*. Chyla has shown that this is not quite true. Here we define a proper RG invariant, the "effective exponent" gamma(Q), whose fixed-point limit is the true gamma*. 
P. M. Stevenson
hep-ph hep-th