  We consider a highly anisotropic $d=2$ Ising spin model whose precise
definition can be found at the beginning of Section 2. In this model the spins
on a same horizontal line (layer) interact via a $d=1$ Kac potential while the
vertical interaction is between nearest neighbors, both interactions being
ferromagnetic. The temperature is set equal to 1 which is the mean field
critical value, so that the mean field limit for the Kac potential alone does
not have a spontaneous magnetization. We compute the phase diagram of the full
system in the Lebowitz-Penrose limit showing that due to the vertical
interaction it has a spontaneous magnetization. The result is not covered by
the Lebowitz-Penrose theory because our Kac potential has support on regions of
positive codimension.
