Critical parameters of N-vector spin models on 3d lattices from high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also denoted as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] have been extended to order beta^{21} on the simple cubic and the body centered cubic lattices, for arbitrary N. The series for the second field derivative of the susceptibility has been extended to order beta^{17}. An analysis of the newly computed series yields updated estimates of the model's critical parameters in good agreement with present renormalization group estimates.Comment: 3 pages, Latex,(fleqn.sty, espcrc2.sty) no figures, contribution to Lattice'97 to appear in Nucl. Phys. Proc. Supp

A remark on the numerical validation of triviality for scalar field theories using high-temperature expansions

We suggest a simple modification of the usual procedures of analysis for the high-temperature (strong-coupling or hopping-parameter) expansions of the renormalized four-point coupling constant in the fourdimensional phi^4 lattice scalar field theory. As a result we can more convincingly validate numerically the triviality of the continuum limit taken from the high temperature phase.Comment: 8 pages, latex, 2 figure