  The Ising model in a random field and with power-law decaying ferromagnetic
bonds is studied at zero temperature. Comparing the scaling of the energy
contributions of the ferromagnetic domain wall flip and of the random field a
la Imry-Ma we obtain a threshold value for the power $\rho$ of the long-range
interaction, beyond which no critical behavior occurs. The critical threshold
value is $\rho_c=3/2$, at a difference with the zero field model in which
$\rho_c=2$. This prediction is confirmed by numerical computation of the ground
states below, at, and above this threshold value. Some possible implications
for the critical behavior of spin-glasses in a field are conjectured.
