  In this article we study the phase transition phenomenon for the Ising model
under the action of a non-uniform external magnetic field. We show that the
Ising model on the hypercubic lattice with a summable magnetic field has a
first-order phase transition and, for any positive (resp. negative) and bounded
magnetic field, the model does not present the phase transition phenomenon
whenever $\liminf h_i> 0$, where ${\bf h} = (h_i)_{i \in \Z^d}$ is the external
magnetic field.
