A Two-Parameter Recursion Formula For Scalar Field Theory

Abstract

We present a two-parameter family of recursion formulas for scalar field theory. The first parameter is the dimension $(D)$. The second parameter ($ζ$) allows one to continuously extrapolate between Wilson's approximate recursion formula and the recursion formula of Dyson's hierarchical model. We show numerically that at fixed $D$, the critical exponent $γ$ depends continuously on $ζ$. We suggest the use of the $ζ-$independence as a guide to construct improved recursion formulas.