Renormalized couplings and scaling correction amplitudes in theN-vector spin models on the sc and the bcc lattices

1998/05/26 by P. Butera, M. Comi · 2 citations
Mathematics · Physics and Astronomy · #Amplitude #Condensed matter physics #Geometry #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Scaling #Scaling law #Spin (aerodynamics) #Statistical physics #Theoretical and Computational Physics #Thermodynamics #cond-mat #hep-lat

paper · pdf · doi:10.1103/physrevb.58.11552

published as Phys.Rev. B58 (1998) 11552-11569 · 23 pages, latex, no figures

arxiv created 1998/05/26 · openalex publication_date 1998/11/01 · openalex created_date 2016/06/24 · arxiv updated 2016/09/01 · openalex updated_date 2026/08/05

Abstract

For the classical N-vector model, with arbitrary N, we have computed through order \ensuremathβ¹⁷ the high-temperature expansions of the second field derivative of the susceptibility \ensuremathχ₄(N,\ensuremathβ) on the simple cubic and on the body centered cubic lattices. [The N-vector model is also known as the O(N) symmetric classical spin Heisenberg model or, in quantum field theory, as the lattice O(N) nonlinear \ensuremathσ model.] By analyzing the expansion of \ensuremathχ₄(N,\ensuremathβ) on the two lattices, and by carefully allowing for the corrections to scaling, we obtain updated estimates of the critical parameters and more accurate tests of the hyperscaling relation d\ensuremathν(N)+\ensuremathγ(N)\ensuremath-2\ensuremathΔ₄(N)=0 for a range of values of the spin dimensionality N, including N=0 (the self-avoiding walk model), N=1 (the Ising spin 1/2 model), N=2 (the XY model), N=3 (the classical Heisenberg model). Using the recently extended series for the susceptibility and for the second correlation moment, we also compute the dimensionless renormalized four point coupling constants and some universal ratios of scaling correction amplitudes in fair agreement with recent renormalization group estimates.

Citations

• Critical exponents of the classical three-dimensional Heisenberg model: A single-cluster Monte Carlo study
• Four-point renormalized coupling constant and Callan-Symanzik β-function in O(N) models
• Ising Universality in Three Dimensions: A Monte Carlo Study
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Monte Carlo computation of the effective potential for the three dimensional Ising system
• Critical temperatures of the d=3, s=1/2Ising model; the effect of confluent corrections to scaling
• Critical exponents of theN-vector model
• The Magnetization of the 3D Ising Model

Cited by

• Eliminating leading corrections to scaling in the three-dimensionalO(N)-symmetric ϕ4model:N= 3 and 4
• Free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model