Anisotropic Ising Model in d plus s Dimensions

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 Js>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.