Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models

Abstract

The effect of the $\ord{\partial^4}$ terms of the gradient expansion on anomalous dimension $\eta$ and the correlation length's critical exponent $\nu$ of the Wilson-Fisher fixed point has been determined for the Euclidean $O(N)$ model for $N=1$ and the number of dimensions $2<d<4$ as well as for $N\ge 2$ and $d=3$. Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory for $N\ge 2$ is well approximated by the effective average action preserving $O(N)$ symmetry with the accuracy of $\ordη$.

arXiv comment19 pages, 27 figures

References in corpus (52)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Critical Exponents of the N-vector model
• Optimised Renormalisation Group Flows
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• Optimisation of the exact renormalisation group
• Quantum Field Theory in the Large N Limit: a review
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Critical Exponents from the Effective Average Action
• Derivative Expansion of the Exact Renormalization Group
• The critical exponents of the superfluid transition in He4
• 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
• A new method to solve the Non Perturbative Renormalization Group equations
• Critical exponents for 3D O(n)-symmetric model with n > 3
• Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition
• Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
• Completeness and consistency of renormalisation group flows
• Ising exponents from the functional renormalisation group
• Scheme Independence and the Exact Renormalization Group
• On the Connection Between Momentum Cutoff and Operator Cutoff Regularizations
• Derivative expansion and renormalisation group flows
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Solutions of renormalization group flow equations with full momentum dependence
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• Perturbation theory and renormalisation group equations
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Optimization of Renormalization Group Flow
• Predictive power of renormalisation group flows: a comparison
• Universality and the Renormalisation Group
• Coarse graining and first order phase transitions
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Polchinski equation, reparameterization invariance and the derivative expansion
• Proper time regulator and Renormalization Group flow
• Critical Phenomena in Continuous Dimension
• Subleading critical exponents from the renormalisation group
• The heat-kernel and the average effective potential
• Global Wilson-Fisher fixed points
• Fixed points and the spontaneous breaking of scale invariance
• Critical $O(N)$ models in the complex field plane
• Equation of state near the endpoint of the critical line
• Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values"
• Towards Functional Flows for Hierarchical Models
• Interplay of fixed points in scalar models
• Enhancement of field renormalization in scalar theories via functional renormalization group
• Renormalization-Group flow for the field strength in scalar self-interacting theories

Cited by in corpus (1)

• Derivative expansion for computing critical exponents of O(N) symmetric models at NNLO