Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion

Abstract

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this expansion applied to the Wilson-Polchinski equation in the case of the $N$-vector model with the symmetry $\mathrm{O}(N)$. As a test, the critical exponents and $\nu$ as well as the subcritical exponent $\omega$ (and higher ones) are estimated in three dimensions for values of $N$ ranging from 1 to 20. I compare the results with the corresponding estimates obtained in preceding studies or treatments of other $\mathrm{O}(N)$ exact RG equations at second order. The possibility of varying $N$ allows to size up the derivative expansion method. The values obtained from the resummation of high orders of perturbative field theory are used as standards to illustrate the eventual convergence in each case. A peculiar attention is drawn on the preservation (or not) of the reparametrisation invariance.

Dedicated to Lothar Schäfer on the occasion of his 60th birthday. Final version

References in corpus (34)

• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Optimisation of the exact renormalisation group
• Exact Renormalization Group Equations. An Introductory Review
• Critical Exponents from the Effective Average Action
• Derivative Expansion of the Exact Renormalization Group
• Lectures on the functional renormalization group method
• Critical exponents from optimised renormalisation group flows
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Mind The Gap
• Critical exponents for 3D O(n)-symmetric model with n > 3
• Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
• Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition
• Scheme Independence and the Exact Renormalization Group
• Seven-Loop Critical Exponents from Strong-Coupling phi^4-Theory in Three Dimensions
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Towards an accurate determination of the critical exponents with the Renormalization Group flow equations
• The Renormalization Group and Two Dimensional Multicritical Effective Scalar Field Theory
• Renormalization Group Flow Equations and the Phase Transition in O(N)-models
• Rapidly Converging Truncation Scheme of the Exact Renormalization Group
• O(N) models within the local potential approximation
• Polchinski equation, reparameterization invariance and the derivative expansion
• Proper time regulator and Renormalization Group flow
• Critical Phenomena in Continuous Dimension
• Non Perturbative Renormalization Group, momentum dependence of $n$-point functions and the transition temperature of the weakly interacting Bose gas
• Optimization of field-dependent nonperturbative renormalization group flows
• Equation of state near the endpoint of the critical line
• The Wilson-Polchinski exact renormalization group equation
• Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory
• Exact renormalization group equation for the Lifshitz critical point
• Exact renormalization group flow equations for free energies and N-point functions in uniform external fields
• What can be learnt from the nonperturbative renormalization group?
• The Effective Average Action Beyond First Order
• Functional renormalization group in the two-dimensional Hubbard model

Cited by in corpus (13)

• An Introduction to the Nonperturbative Renormalization Group
• Fundamentals of the Exact Renormalization Group
• Ising exponents from the functional renormalisation group
• Lectures on renormalization and asymptotic safety
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Asymptotic safety of scalar field theories
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Critical exponents of the O(N) model in the infrared limit from functional renormalization
• Revisiting the local potential approximation of the exact renormalization group equation
• Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation
• Quantum-classical transition in the Caldeira-Leggett model
• Phase structure of the $O(2)$ ghost model with higher-order gradient term
• Triple point in the $O(2)$ ghost model with higher-order gradient term