A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping t\&$\#$39;=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite t\&$\#$39; and at t\&$\#$39;=0 but for two totally different physical reasons. When t\&$\#$39;=0, it is induced by antiferromagnetic correlations while at t\&$\#$39;=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.

}, author = {Veilleux, A. F. and Dare, A. M. and Chen, L. A. and Vilk, Y.M. and A.-M. S. Tremblay} }