Five-loop renormalization group functions of $O(n)$-symmetric ${\varphi }^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$

Abstract

Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the $\beta$-function and the anomalous dimensions of the $O(n)$-symmetric ${\varphi }^4$-theory in $D=4-\ep$ dimensions we present the results of a full analytic reevaluation of all diagrams. The divergences are removed by minimal subtraction and $\ep$-expansions are given for the critical exponents $\eta$, $\nu$, and $\omega$ up to order ${\epsilon }^5$.

LaTeX file. For related work see the www address http://www.physik.fu-berlin.de/kleiner_re.html on our www homepage http://www.physik.fu-berlin.de/kleinert.html

Cited by in corpus (97)

• Critical Exponents of the N-vector model
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Critical behavior of the three-dimensional XY universality class
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Avalanches, Barkhausen Noise, and Plain Old Criticality
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• 3D Ising Model:The Scaling Equation of State
• Disorder-Induced Critical Phenomena in Hysteresis: Numerical Scaling in Three and Higher Dimensions
• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• On the definition of a unique effective temperature for non-equilibrium critical systems
• Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
• Numbers and Functions in Quantum Field Theory
• Effective Action, Conformal Anomaly and the Issue of Quadratic Divergences
• Exact Five-Loop Renormalization Group Functions of ${\varphi }^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$
• Screened Perturbation Theory to Three Loops
• Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series
• Four loop renormalization of the Gross-Neveu model
• Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ${\epsilon }^{1/2}$-Expansion
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Six loop analytical calculation of the field anomalous dimension and the critical exponent $\eta$ in $O(n)$-symmetric ${\phi }^4$ model
• Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices
• Mass Expansions of Screened Perturbation Theory
• Viable dark matter via radiative symmetry breaking in a scalar singlet Higgs portal extension of the standard model
• Scale Setting for Self-consistent Backgrounds
• Four-loop screened perturbation theory
• Multi-loop techniques for massless Feynman diagram calculations
• On critical exponents without Feynman diagrams
• Pade-Improvement of QCD Running Coupling Constants, Running Masses, Higgs Decay Rates, and Scalar Channel Sum Rules
• Five-loop epsilon expansion for O(n)xO(m) spin models
• Stability of a cubic fixed point in three dimensions. Critical exponents for generic N
• Radiative Electroweak Symmetry-Breaking Revisited
• Critical Phenomena in Continuous Dimension
• A Prediction for the 4-Loop βFunction
• Recursive Graphical Construction of Feynman Diagrams and Their Multiplicities in phi^4- and in phi^2A-Theory
• Closed-Form Summation of RG-Accessible Logarithmic Contributions to Semileptonic B-Decays and Other Perturbative Processes
• Extension to order ${\beta }^{23}$ of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices
• Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions
• Critical specific heats of the N-vector spin models on the sc and the bcc lattices
• Five-loop epsilon expansion for U(n)xU(m) models: finite-temperature phase transition in light QCD
• Field theory of bi- and tetracritical points: Statics
• Optimal Renormalization-Group Improvement of Two Radiatively-Broken Gauge Theories
• Solution to the 3-Loop $\Phi$-Derivable Approximation for Massless Scalar Thermodynamics
• A simple way to generate high order vacuum graphs
• Four-Loop Vacuum Energy Beta Function in O(N) Symmetric Scalar Theory
• Three-dimensional antiferromagnetic CP(N-1) models
• The normal-to-planar superfluid transition in Helium 3
• Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors
• Five-Loop Vacuum Energy Beta Function in phi^4 Theory with O(N)-Symmetric and Cubic Interactions
• Is Radiative Electroweak Symmetry Breaking Consistent with a 125 GeV Higgs Mass?
• Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster
• Field Theories for Loop-Erased Random Walks
• Renormalization Group Optimized Perturbation Theory at Finite Temperatures
• Crossover exponent in O(N) phi^4 theory at O(1/N^2)
• The critical equation of state of the three-dimensional O(N) universality class: N>4
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• Renormalization group improvement of the effective potential in massive ${\varphi }^4$ theory
• Can the Renormalization Group Improved Effective Potential be used to estimate the Higgs Mass in the Conformal Limit of the Standard Model?
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory
• A Unique Determination of the Effective Potential in Terms of Renormalization Group Functions
• Quantum implications of a scale invariant regularisation
• Mean-field expansion for spin models with medium-range interactions
• Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy
• Critical exponents of the O(N) model in the infrared limit from functional renormalization
• Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion
• Stability of Subsequent-to-Leading-Logarithm Corrections to the Effective Potential for Radiative Electroweak Symmetry Breaking
• Higher Order Stability of a Radiatively Induced 220 GeV Higgs Mass
• Universality classes of three-dimensional $mn$-vector model
• Critical exponent omega at O(1/N) in O(N) x O(m) spin models
• Chiral exponents in O(N) x O(m) spin models at O(1/N^2)
• Higher dimensional higher derivative ${\varphi }^4$ theory
• Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric ${\varphi }^4$ theory with $n\to -2$ and loop-erased random walks
• Precise Critical Exponents of the O(N)-Symmetric Quantum field Model using Hypergeometric-Meijer Resummation
• Conformal Bootstrap Signatures of the Tricritical Ising Universality Class
• Numerical study of the enlarged O(5) symmetry of the 3-D antiferromagnetic RP2 spin model
• Resummations of free energy at high temperature
• Progress with large N_f beta-functions
• Study of the Six-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme
• Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps
• Robustness of the O($N$) universality class
• Recursive Graphical Solution of Closed Schwinger-Dyson Equations in phi^4-Theory -- Part1: Generation of Connected and One-Particle Irreducible Feynman Diagrams
• Study of the Question of an Ultraviolet Zero in the Six-Loop Beta Function of the O($N$) $\lambda |\vec{\varphi }{|}^4$ Theory
• Renormalization group approach for Lorentz-violating scalar field theory at all loop orders
• The epsilon-expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature
• Scaling of star polymers: high order results
• The Derivative Expansion of the Effective Action and the Renormalization Group Equation
• Five loop renormalization of the Wess-Zumino model
• Model C critical dynamics of random anisotropy magnets
• Estimate of the Three-Loop MS bar Contribution to sigma(W_L^+ W_L^- --> Z_L Z_L)
• Perturbative reliability of the Higgs-boson coupling in the standard electroweak model
• Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory
• Renormalization Group Functions for the Radiative Symmetry Breaking Scheme
• Phase diagram of Model C in the parametric space of order parameter and space dimensions
• Diminished Upper Bounds on the Unification Mass Scales for Heavy Higgs Boson Masses