Critical specific heats of the N-vector spin models on the sc and the bcc lattices

Details Critical specific heats of the N-vector spin models on the sc and the bcc lattices Critical specific heats of the N-vector spin models on the sc and the bcc lattices

1999-03-04

arxiv.org/abs/hep-lat/9903010v1

Phys.Rev. B60 (1999) 6749

Physics

High Energy Physics

High Energy Physics - Lattice

15 pages, latex, no figures

Scientific paper

10.1103/PhysRevB.60.6749

We have computed through order $\beta^{21}$ the high-temperature expansions for the nearest-neighbor spin correlation function $G(N,\beta)$ of the classical N-vector model, with general N, on the simple-cubic and on the body-centered-cubic lattices. For this model, also known in quantum field theory as the lattice O(N) nonlinear sigma model, we have presented in previous papers extended expansions of the susceptibility, of its second field derivative and of the second moment of the correlation function. Here we study the internal specific energy and the specific heat $C(N,\beta)$, obtaining new estimates of the critical parameters and therefore a more accurate direct test of the hyperscaling relation $d \nu(N)=2 - \alpha(N)$ on 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]. By the newly extended series, we also compute the universal combination of critical amplitudes usually denoted by $R^+_{\xi}(N)$, in fair agreement with renormalization group estimates.

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