  In this note, we consider the asymmetric nearest neighbor ferromagnetic Ising
model on the $(d+s)$-dimensional unit cubic lattice $\Z^{d+s}$, at inverse
temperature $\beta=1$ and with coupling constants $J_s>0$ and $J_d>0$ for edges
of $\Z^s$ and $\Z^d$, respectively. We obtain a lower bound for the critical
curve in the phase diagram of $(J_s,J_d)$. In particular, as $J_d$ approaches
its critical value from below, our result is directly related to the so-called
dimensional crossover phenomenon.
