The model introduced by Van den Broeck, Parrondo and Toral [Phys.
Rev. Lett. { f 73}, 3395 (1994)]---leading to a second-order-like
{em noise-induced nonequilibrium phase transition/} which shows {em
reentrance/} as a function of the (multiplicative) noise intensity
$sigma$---is investigated beyond the white-noise assumption. Through
a Markovian approximation and within a mean-field treatment it is
found that---in striking contrast with the usual behavior for
equilibrium phase transitions---for noise self-correlation time
$ au>0$, the {em stable/} phase for (diffusive) spatial coupling
$D oinfty$ is always the {em disordered/} one. Another surprising
result is that a large noise memory also tends to {em destroy/}
order. These results are supported by numerical simulations.
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