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

Abstract

For the classical N-vector model, with arbitrary N, we have computed through order β^{17} the high temperature expansions of the second field derivative of the susceptibility χ_4(N,β) 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 sigma model.) By analyzing the expansion of χ_4(N,β) 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 dν(N) +γ(N) -2Δ_4(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.

23 pages, latex, no figures

References in corpus (5)

• Critical Exponents of the N-vector model
• Critical exponents for 3D O(n)-symmetric model with n > 3
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• Perturbative renormalization group, exact results and high temperature series to order 21 for the N-vector spin models on the square lattice
• Monte Carlo results for three-dimensional self-avoiding walks

Cited by in corpus (40)

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• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
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• Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
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