Universal sextic effective interaction at criticality

Abstract

The renormalization group approach in three dimensions is used to estimate the universal critical value g_6^* of the dimensionless sextic effective coupling constant for the Ising model. The four-loop RG expansion for g_6 is calculated and resummed by means of the Pade-Borel and Pade-Borel-Leroy procedures resulting in g_6^* = 1.596, while the most accurate estimate for g_6^* is argued to be equal to 1.61.

6 pages, TeX, no figures

References in corpus (3)

• Addendum-erratum to: ``Nonasymptotic critical behavior from field theory at d=3. II. The ordered-phase case. Phys. Rev. B35, 3585 (1987)
• Critical exponents for 3D O(n)-symmetric model with n > 3
• Phase transitions in anisotropic superconducting and magnetic systems with vector order parameters: Three-loop renormalization-group analysis

Cited by in corpus (14)

• Critical Exponents of the N-vector model
• Effective potential in three-dimensional O(N) models
• The effective potential of N-vector models: a field-theoretic study to O(ε^3)
• Universal critical coupling constants for the three-dimensional n-vector model from field theory
• Renormalized sextic coupling constant for the two-dimensional Ising model from field theory
• The free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model
• Renormalization group and nonlinear susceptibilities of cubic ferromagnets at criticality
• Pseudo-epsilon expansion and the two-dimensional Ising model
• Pseudo-$\epsilon$ Expansion and Renormalized Coupling Constants at Criticality
• Duality symmetry, strong coupling expansion and universal critical amplitudes in two-dimensional Φ^{4} field models
• Critical renormalized coupling constants in the symmetric phase of the Ising models
• Effective potential of the three-dimensional Ising model: the pseudo-$\epsilon$ expansion study
• Nonlinear susceptibilities of a weakly-disordered uniaxial ferromagnet in the critical region
• Universal effective couplings of the three-dimensional $n$-vector model and field theory