Renormalization Group and Universality

Abstract

It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$ scalar field theory. Our equations are superior compared with the usual approach which retains only the contributions that are non-vanishing in the ultraviolet regime. We find an indication for the existence of relevant operators at the infrared fixed point, contrary to common expectations. This result makes the sufficiency of using only renormalizable coupling constants in parametrizing the long distance phenomena questionable.

32pp in plain tex; revised version to appear in PRD

References in corpus (4)

• Derivative Expansion of the Exact Renormalization Group
• On Truncations of the Exact Renormalization Group
• Renormalizability of Effective Scalar Field Theory
• Critical Exponents without the Epsilon Expansion

Cited by in corpus (28)

• Aspects of the Functional Renormalisation Group
• Exact Renormalization Group Equations. An Introductory Review
• On the Connection Between Momentum Cutoff and Operator Cutoff Regularizations
• Towards an accurate determination of the critical exponents with the Renormalization Group flow equations
• Optimization of Renormalization Group Flow
• On the Convergence of the Expansion of Renormalization Group Flow Equation
• Momentum Scale Expansion of Sharp Cutoff Flow Equations
• Renormalization Group Approach to Field Theory at Finite Temperature
• Functional Callan-Symanzik equation for QED
• The renormalization group flow of the dilaton potential
• Scaling functions for the O(4)-model in d=3 dimensions
• The antiferromagnetic phi4 Model, I. The Mean-field Solution
• Finite-Size Scaling behavior in the O(4)-Model
• Global Renormalization Group
• Dimensional Crossover and Effective Exponents
• The beta functions of a scalar theory coupled to gravity
• Two loop results from the derivative expansion of the blocked action
• Non-perturbative renormalization group approach for a scalar theory in higher-derivative gravity
• Gauge Consistent Wilson Renormalization Group I: Abelian Case
• Exact renormalization group study of fermionic theories
• Anti-Ferromagnetic Condensate in Yang-Mills Theory
• Differential Renormalization-Group Approach to the Layered sine-Gordon Model
• Scheme Independence of Blocking Transformation in Finite-Temperature Renormalization Group
• Gauge Invariant Cutoff QED
• Functional renormalization of N scalars with O(N) invariance
• Fixed point analysis of a scalar theory with an external field
• Flow Equations for U_k and Z_k
• Non-Trivial Fixed Points of the Scalar Field Theory