The regulator dependence in the functional renormalization group: a quantitative explanation

Abstract

The search of controlled approximations to study strongly coupled systems remains a very general open problem. Wilson's renormalization group has shown to be an ideal framework to implement approximations going beyond perturbation theory. In particular, the most employed approximation scheme in this context, the derivative expansion, was recently shown to converge and yield accurate and very precise results. However, this convergence strongly depends on the shape of the employed regulator. In this letter we clarify the reason for this dependence and justify, simultaneously, the most largely employed procedure to fix this dependence, the principle of minimal sensitivity.

arXiv comment6 pages, 2 figures, accepted in Physical Review E

References in corpus (18)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• The Exact Renormalisation Group and Approximate Solutions
• The nonperturbative functional renormalization group and its applications
• Optimisation of the exact renormalisation group
• Critical exponents from optimised renormalisation group flows
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• A new method to solve the Non Perturbative Renormalization Group equations
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Scheme dependence and universality in the functional renormalization group
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Three-dimensional $O(N)$-invariant ${\varphi }^4$ models at criticality for $N\ge 4$
• Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO

Cited by in corpus (9)

• Functional renormalisation group for turbulence
• Regulator scheme dependence of the chiral phase transition at high densities
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• The $q-$state Potts model from the Nonperturbative Renormalization Group
• Stochastic dynamics for Group Field Theories
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems