A Two-Parameter Recursion Formula For Scalar Field Theory
نویسندگان
چکیده
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.
منابع مشابه
A ug 1 99 6 U . of Iowa preprint 96 - 11 A Two - Parameter Recursion Formula For Scalar Field Theory
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 recur-sion 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 us...
متن کاملX iv : h ep - t h / 96 09 05 7 v 1 6 S ep 1 99 6 U . of Iowa preprint 96 - 13 NON - PERTURBATIVE ASPECTS OF SCALAR FIELD THEORY ∗
Using the hierarchical approximation, we discuss the cut-off dependence of the renormalized quantities of a scalar field theory. The naturalness problem and questions related to triviality bounds are briefly discussed. We discuss unphysical features associated with the hierarchical approximation such as the recently observed oscillatory corrections to the scaling laws. We mention a two-paramete...
متن کاملNonlinear Aspects of the Renormalization Group Flows of Dyson’s Hierarchical Model
We review recent results concerning the renormalization group (RG) transformation of Dyson’s hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notati...
متن کامل/ 05 08 54 2 v 2 19 O ct 2 00 5 Reconstruction of general scalar - field dark energy models
The reconstruction of scalar-field dark energy models is studied for a general Lagrangian density p(φ,X), where X is a kinematic term of a scalar field φ. We implement the coupling Q between dark energy and dark matter and express reconstruction equations using two observables: the Hubble parameter H and the matter density perturbation δm. This allows us to determine the structure of correspond...
متن کاملCasimir effects of nano objects in fluctuating scalar and electromagnetic fields: Thermodynamic investigating
Casimir entropy is an important aspect of casimir effect and at the nanoscale is visible. In this paper, we employ the path integral method to obtain a general relation for casimir entropy and internal energy of arbitrary shaped objects in the presence of two, three and four dimension scalar fields and the electromagnetic field. For this purpose, using Lagrangian and based on a perturb...
متن کامل