# Renormalization group functional equations.

@article{Curtright2011RenormalizationGF, title={Renormalization group functional equations.}, author={T. Curtright and C. Zachos}, journal={Physical Review D}, year={2011}, volume={83}, pages={065019} }

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 step-scaling {sigma} functions and lead to exact functional relations for the local flow {beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {sigma} are… Expand

#### 18 Citations

Volume Effects in Discrete beta functions

- Physics
- 2011

We calculate discrete beta functions corresponding to the two-lattice matching for the 2D O(N) models and Dyson's hierarchical model. We describe and explain finite-size effects such as the… Expand

New applications of the renormalization group method in physics: a brief introduction

- Physics, Medicine
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2011

The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics, in a way that emphasizes common themes and the universal aspects of the method. Expand

RG flows, cycles, and c-theorem folklore

- Physics, Mathematics
- 2011

Monotonic renormalization group flows of the “c” and “a” functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples,… Expand

Renormalization group flows, cycles, and c-theorem folklore.

- Mathematics, Medicine
- Physical review letters
- 2012

It is argued here, based on simple examples, that simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings. Expand

Branched Hamiltonians and supersymmetry

- Physics, Mathematics
- 2014

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback… Expand

Approximate solutions of functional equations

- Mathematics, Physics
- 2011

Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both… Expand

Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories

- Physics
- 2013

In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization… Expand

Potentials unbounded below

- Mathematics, Physics
- 2011

Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The… Expand

Large-spin expansions of GKP strings

- Physics
- 2014

A bstractWe demonstrate that the large-spin expansion of the energy of Gubser-Klebanov-Polyakov (GKP) strings that rotate in ℝ × S2 and AdS3 can be expressed in terms of Lambert’s W-function. We… Expand

Perturbative QCD Invariant Charge

- Physics
- 2017

This chapter delineates the perturbative strong running coupling and its basic features. In particular, this chapter describes the renormalization group equation for the QCD invariant charge,… Expand

#### References

SHOWING 1-10 OF 47 REFERENCES

Small distance behaviour in field theory and power counting

- Mathematics
- 1970

For infinitesimal changes of vertex functions under infinitesimal variation of all renormalized parameters, linear combinations are found such that the net infinitesimal changes of all vertex… Expand

Renormalization group limit cycles and field theories for ellipticS-matrices

- Physics, Mathematics
- 2004

The renormalization group (RG) for maximally anisotropic su(2) current interactions in two dimensions is shown to be cyclic at one-loop level. The fermionized version of the model exhibits… Expand

Russian doll renormalization group and Kosterlitz–Thouless flows

- Physics
- 2003

Abstract We investigate the previously proposed cyclic regime of the Kosterlitz–Thouless renormalization group (RG) flows. The period of one cycle is computed in terms of the RG invariant. Using… Expand

Renormalization Group and Strong Interactions

- Physics
- 1971

The renormalization-group method of Gell-Mann and Low is applied to field theories of strong interactions. It is assumed that renormalization-group equations exist for strong interactions which… Expand

Limit cycles in quantum theories.

- Physics, Medicine
- Physical review letters
- 2002

This work discusses the simplest quantum model Hamiltonian identified so far that exhibits a renormalization group with both limit cycle and chaotic behavior, a discrete Hermitian matrix with two coupling constants. Expand

Critical Behavior in Two-dimensional Quantum Gravity and Equations of Motion of the String

- Physics
- 1990

We show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to… Expand

Universality, marginal operators, and limit cycles

- Mathematics, Physics
- 2004

The universality of renormalization-group limit-cycle behavior is illustrated with a simple discrete Hamiltonian model. A nonperturbative renormalization-group equation for the model is soluble… Expand

Log-periodic behavior of finite size effects in field theories with RG limit cycles

- Physics
- 2004

Abstract We compute the finite size effects in the ground state energy, equivalently the effective central charge c eff , based on S-matrix theories recently conjectured to describe a cyclic regime… Expand

Torsion and geometrostasis in nonlinear sigma models

- Physics
- 1985

Abstract We discuss some general effects produced by adding Wess-Zumino terms to the actions of nonlinear sigma models, an addition which may be made if the underlying field manifold has appropriate… Expand

Small-distance-behaviour analysis and Wilson expansions

- Mathematics
- 1971

A previously described method to obtain the asymptotic forms of vertex functions at large momenta is, with the help of Wilson operator product expansion formulas, extended to momenta where the vertex… Expand