  We consider self-avoiding walk and percolation in $\Zd$, oriented percolation
in $\Zd\times\Zp$, and the contact process in $\Zd$, with $p D(\cdot)$ being
the coupling function whose range is denoted by $L<\infty$. For percolation,
for example, each bond $\{x,y\}$ is occupied with probability $p D(y-x)$. The
above models are known to exhibit a phase transition when the parameter $p$
varies around a model-dependent critical point $\pc$. We investigate the value
of $\pc$ when $d>6$ for percolation and $d>4$ for the other models, and
$L\gg1$. We prove in a unified way that $\pc=1+C(D)+O(L^{-2d})$, where the
universal term 1 is the mean-field critical value, and the model-dependent term
$C(D)=O(L^{-d})$ is written explicitly in terms of the function $D$. Our proof
is based on the lace expansion for each of these models.
