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The local, uncorrelated multiplicative noises driving a second-order, purelynoise-induced, ordering phase transition (NIPT) were assumed to be Gaussian andwhite in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. Thepotential scientific and technological interest of this phenomenon calls for astudy of the effects of the noises' statistics and spectrum. This task isfacilitated if these noises are dynamically generated by means of stochasticdifferential equations (SDE) driven by white noises. One such case is that ofOrnstein--Uhlenbeck noises which are stationary, with Gaussian pdf and avariance reduced by the self-correlation time (\tau), and whose effect on theNIPT phase diagram has been studied some time ago. Another such case is whenthe stationary pdf is a (colored) Tsallis' (q)--\emph{Gaussian} which, being a\emph{fat-tail} distribution for (q>1) and a \emph{compact-support} one for(q<1), allows for a controlled exploration of the effects of the departure fromGaussian statistics. As done before with stochastic resonance and otherphenomena, we now exploit this tool to study--within a simple mean-fieldapproximation and with an emphasis on the \emph{order parameter} and the``\emph{susceptibility}''--the combined effect on NIPT of the noises'statistics and spectrum. Even for relatively small (\tau), it is shown thatwhereas fat-tail noise distributions ((q>1)) counteract the effect ofself-correlation, compact-support ones ((q<1)) enhance it. Also, an interestingeffect on the susceptibility is seen in the last case.

Noise-induced phase transitions: Effects of the noises' statistics and spectrum