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The Ising model in a random field and with power-law decaying ferromagneticbonds is studied at zero temperature. Comparing the scaling of the energycontributions of the ferromagnetic domain wall flip and of the random field ala Imry-Ma we obtain a threshold value for the power $\rho$ of the long-rangeinteraction, beyond which no critical behavior occurs. The critical thresholdvalue 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 groundstates below, at, and above this threshold value. Some possible implicationsfor the critical behavior of spin-glasses in a field are conjectured.

Imry-Ma criterion for long-range random field Ising model: short-/long-range equivalence in a field