  The phase transitions that occur in an infinite-range-interaction Ising
ferromagnet in the presence of a double-Gaussian random magnetic field are
analyzed. Such random fields are defined as a superposition of two Gaussian
distributions, presenting the same width $\sigma$. Is is argued that this
distribution is more appropriate for a theoretical description of real systems
than its simpler particular cases, i.e., the bimodal ($\sigma=0$) and the
single Gaussian distributions. It is shown that a low-temperature first-order
phase transition may be destructed for increasing values of $\sigma$, similarly
to what happens in the compound $Fe_{x}Mg_{1-x}Cl_{2}$, whose
finite-temperature first-order phase transition is presumably destructed by an
increase in the field randomness.
