Spatial patterns induced by additive noise

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Abstract
We consider a nonlinear lattice with spatial coupling under the influence of multiplicative and additive noise. In contrast to other studies, we pay attention mainly to the role of the additive noise and show that additive noise, much like multiplicative noise, is able to induce spatial patterns. The reason is that the increase of additive noise causes a nonequilibrium phase transition that manifests itself in the formation of ordered spatial patterns. The presence of the additive noise correlated or uncorrelated with the multiplicative noise is a necessary condition of the phase transition. We review the mean field theory for this model and show that this theory predicts a reentrant phase transition caused by additive noise. Theoretical predictions are confirmed by numerical simulations.