Universal effective couplings of the three-dimensional n-vector model and field theory

2019/09/30 by A. Kudlis, A. I. Sokolov
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Combinatorics #Complex Systems and Time Series Analysis #Coupling (piping) #Coupling constant #Curse of dimensionality #Field (mathematics) #Loop (graph theory) #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum chromodynamics #Quantum mechanics #Renormalization #Renormalization group #Resummation #Series (stratigraphy) #Spectroscopy and Quantum Chemical Studies #Spin (aerodynamics) #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.nuclphysb.2019.114881

openalex created_date 2019/09/19 · openalex publication_date 2019/11/29 · arxiv created 2020/01/21 · arxiv updated 2020/01/22 · openalex updated_date 2026/08/05

Abstract

We calculate the universal ratios R2k of renormalized coupling constants g2k entering the critical equation of state for the generalized Heisenberg (three-dimensional n-vector) model. Renormalization group (RG) expansions of R8 and R10 for arbitrary n are found in the four-loop and three-loop approximations respectively. Universal octic coupling R8⁎ is estimated for physical values of spin dimensionality n=0,1,2,3 and for n=4,...64 to get an idea about asymptotic behavior of R8⁎. Its numerical values are obtained by means of the resummation of the RG series and within the pseudo-ε expansion approach. Regarding R10 our calculations show that three-loop RG and pseudo-ε expansions possess big and rapidly growing coefficients for physical values of n what prevents getting fair numerical estimates.

Citations

• Pseudo-ϵ expansion and critical exponents of superfluid helium
• Four-point renormalized coupling constant and Callan-Symanzik β-function in O(N) models
• Critical exponents from the effective average action
• Precise determination of critical exponents and equation of state by field theory methods
• Copolymer networks and stars: Scaling exponents
• 3D Ising model: the scaling equation of state
• Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model
• Renormalized couplings and scaling correction amplitudes in theN-vector spin models on the sc and the bcc lattices
• Critical exponents of theN-vector model
• Effective potential of the three-dimensional Ising model: the pseudo-ε expansion study