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 ($\zeta$) 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 $\gamma$ depends continuously on $\zeta$. We suggest the use of the $\zeta -$independence as a guide to construct improved recursion formulas.

7 pages, uses Revtex, one Postcript figure

References in corpus (2)

• Wilson Renormalization Group Analysis of Theories with Scalars and Fermions
• Evidence for Complex Subleading Exponents from the High-Temperature Expansion of the Hierarchical Ising Model

Cited by in corpus (8)

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• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model
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• Towards Functional Flows for Hierarchical Models
• A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model
• Universality in nontrivial continuum limits: a model calculation
• Universality, Scaling and Triviality in a Hierarchical Field Theory