ClassicalO(N) Heisenberg model: Extended high-temperature series for two, three, and four dimensions

We present simple tables of integers from which it is possible to reconstruct the high-temperature series coefficients through ${\mathrm{\beta }}^{14}$ for the susceptibility, for the second correlation moment, and for the second field derivative of the susceptibility of the O(N) classical Heisenberg model on a simple (hyper)cubic lattice in dimension d=2, 3, and 4 and for any N. To construct the tables we have used the recent extension of the high-temperature series by M. Luscher and P. Weisz and some analytic properties in N that we have derived from the Schwinger-Dyson equations of the O(N) model. We also present a numerical study of these series in the d=2 case. The main results are: (a) the extended series give further support to the Cardy-Hamber-Nienhuis exact formulas for the critical exponents when -2<N<2; (b) for N≥3 there are no indications of any critical point at finite β; (c) the series are consistent with the low-temperature asymptotic forms predicted by the perturbative renormalization group.