1996/09/06 by Y. Meurice, Meurice, Y., S. Niermann +3
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9609057
5 pages, uses Revtex, Talk given at DPF 96
arxiv created 1996/09/06 · arxiv updated 2009/11/30
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-parameter family of recursion formulas which allows one to continuously extrapolate between Wilson's approximate recursion formula and the recursion formula of Dyson's hierarchical model. The parameters are the dimension D and 2zeta, the number of sites integrated in one RG transformation. We show numerically that at fixed D, the critical exponent gamma depends continuously on zeta. We suggest the requirement of zeta -independence as a guide for constructing improved recursion formulas.