The renormalization group mapping in three dimensions

The construction of the quantitative RG mapping [SD89J starts from the perturbation expansion of W(u) evaluated to order uG or from the expansions for r (u) or 2 — l/i/(u) evaluated to order us. These expansions are only asymptotic, but they can be resumed, using the Borel method. Within 

Rigorous integration of the resulting flow equations (of. Sect. 11.4) yields 

Our final expression for the RG mapping therefore reads RG Mapping (d = 3) 

The nonuniversai constants sn can be expressed in terms of the starting value /o = /(A = 1) -as 

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