Four-point renormalized coupling constant in O(N) models

Abstract

The renormalized zero-momentum four-point coupling $g_r$ of O(N)-invariant scalar field theories in $d$ dimensions is studied by applying the 1/N expansion and strong coupling analysis. The O(1/N) correction to the $\beta$-function and to the fixed point value $g_r^{\ast }$ are explictly computed. Strong coupling series for lattice non-linear sigma models are analyzed near criticality in d=2 and d=3 for several values of $N$ and the corresponding values of $g_r^{\ast }$ are extracted. Large-N and strong coupling results are compared with each other, finding a good general agreement. For small N the strong coupling analysis in 2-d gives the best determination of $g_r^{\ast }$ to date (or comparable for N=2,3 with the available Monte Carlo estimates), and in 3-d it is consistent with available ${\varphi }^4$ field theory results.

30 pages + 19 figures in an uuencoded postscript file

References in corpus (4)

• Critical exponents for 3D O(n)-symmetric model with n > 3
• The specific heat of superfluids near the transition temperature
• Scaling behavior of the four-point renormalized coupling constant in the two dimensional O(2) and O(3) non-linear sigma models
• Continuum Limits and Exact Finite-Size-Scaling Functions for One-Dimensional $O(N)$-Invariant Spin Models

Cited by in corpus (40)

• Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
• On the nature of the finite-temperature transition in QCD
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• The two-point correlation function of three-dimensional O(N) models: critical limit and anisotropy
• Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model
• A strong-coupling analysis of two-dimensional O(N) sigma models with N<=2 on square, triangular and honeycomb lattices
• Perturbative renormalization group, exact results and high temperature series to order 21 for the N-vector spin models on the square lattice
• Lattice Abelian-Higgs model with noncompact gauge fields
• Effective potential in three-dimensional O(N) models
• Multicomponent compact Abelian-Higgs lattice models
• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
• Crossover scaling from classical to nonclassical critical behavior
• Does the XY Model have an integrable continuum limit?
• The critical equation of state of three-dimensional XY systems
• Higher-charge three-dimensional compact lattice Abelian-Higgs models
• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Universal critical coupling constants for the three-dimensional n-vector model from field theory
• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• Unexpected results in asymptotically free quantum field theories
• Lattice gauge theories in the presence of a linear gauge-symmetry breaking
• The Intrinsic Coupling in Integrable Quantum Field Theories
• Continuum Limits and Exact Finite-Size-Scaling Functions for One-Dimensional $O(N)$-Invariant Spin Models
• A strong-coupling analysis of two-dimensional O(N) sigma models with $N\ge 3$ on square, triangular and honeycomb lattices
• Critical Exponents in Two Dimensions and Pseudo-ε Expansion
• Linked-Cluster Expansion of the Ising Model
• Pseudo-$\epsilon$ Expansion and Renormalized Coupling Constants at Criticality
• The unreasonable effectiveness of effective string theory: the case of the 3d SU(2) Higgs model
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Critical properties of ${\Phi }_{1+1}^4$-theory in Light-Cone Quantization
• Critical energy density of O$(n)$ models in $d=3$
• Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement
• Effective potential of the three-dimensional Ising model: the pseudo-$\epsilon$ expansion study
• Critical renormalized coupling constants in the symmetric phase of the Ising models
• Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)${}^{\ast }$ and Ising${}^{\ast }$ continuous transitions
• Dynamical Linked Cluster Expansions: A Novel Expansion Scheme for Point-Link-Point-Interactions
• Noncompact sigma-models: Large N expansion and thermodynamic limit
• Hopping Parameter Series Construction for Models with Nontrivial Vacuum
• Universal effective couplings of the three-dimensional $n$-vector model and field theory
• Dynamical Zero Modes and Criticality in Continuous Light Cone Quantization of Phi^{4}_{1+1}
• On the evaluation of the improvement parameter in the lattice Hamiltonian approach to critical phenomena