P. Butera

N vector spin models on the sc and the bcc lattices: A Study of the critical behavior of the susceptibility and of the correlation length by 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 known as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] on the sc and the bcc lattices are extended to order beta^{21} for arbitrary N. The series for the second field derivative of the susceptibility is extended to order beta^{17}. An analysis of the newly computed series for the susceptibility and the (second moment) correlation length yields updated estimates of the critical parameters for various 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 Heisenberg model]. For all values of N, we confirm a good agreement with the present renormalization group estimates. A study of the series for the other observables will appear in a forthcoming paper.

Critical universality and hyperscaling revisited for Ising models of general spin using extended high temperature series

We have extended through

Extended high-temperature series for the N-vector spin models on three-dimensional bipartite lattices.

{\ensuremath{\beta}}^{23}

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

the high-temperature expansion of the second field derivative of the susceptibility for Ising models of general spin, with nearest-neighbor interactions, on the simple cubic and the body-centered cubic lattices. Moreover, the expansions for the nearest-neighbor correlation function, the susceptibility, and the second correlation moment have been extended up to

2N-POINT RENORMALIZED COUPLING CONSTANTS IN THE THREE-DIMENSIONAL ISING MODEL : ESTIMATES BY HIGH TEMPERATURE SERIES TO ORDER BETA 17

{\ensuremath{\beta}}^{25}.

Resolvent operator, padé approximation and bound states in potential seattering

Taking advantage of these new data, we can improve the accuracy of direct estimates of critical exponents and of hyperuniversal combinations of critical amplitudes such as the renormalized four-point coupling

Perturbative renormalization group, exact results and high temperature series to order 21 for the N vector spin models on the square lattice

{g}_{r}

Extension to order β 23 of the high-temperature expansions for the spin- 1 2 Ising model on simple cubic and body-centered cubic lattices

or the quantity usually denoted by

THE RANLUX GENERATOR: RESONANCES IN A RANDOM WALK TEST

{R}_{\ensuremath{\xi}}^{+}.

VARIATIONAL PRINCIPLES AND PADE APPROXIMANTS. BOUND STATES IN POTENTIAL THEORY.

In particular, we obtain