Renormalization group functional equations
Abstract
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods produce continuous flows from stepscaling σ functions and lead to exact functional relations for the local flow β functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of σ are sometimes not true fixed points under continuous changes in scale and zeroes of β do not necessarily signal fixed points of the flow but instead may only indicate turning points of the trajectories.
 Publication:

Physical Review D
 Pub Date:
 March 2011
 DOI:
 10.1103/PhysRevD.83.065019
 arXiv:
 arXiv:1010.5174
 Bibcode:
 2011PhRvD..83f5019C
 Keywords:

 11.10.Gh;
 11.15.Ha;
 11.25.Hf;
 Renormalization;
 Lattice gauge theory;
 Conformal field theory algebraic structures;
 High Energy Physics  Theory;
 High Energy Physics  Lattice;
 Mathematical Physics
 EPrint:
 A physical model with a limit cycle added as section IV, along with references