MESOSCOPIC DESCRIPTION OF THE ANNEALED ISING-MODEL, AND MULTIPLICATIVE NOISE

A new type of Langevin equation exhibiting a nontrivial phase transiti on associated with the presence of multiplicative noise is discussed. The equation is derived as a mesoscopic representation of the microsco pic annealed Ising model (AIM) proposed by Thorpe and Beeman, and repr oduces perfectly its basic phenomenology. The AIM exhibits a nontrivia l behavior as the temperature is increased, in particular it presents a disorder-to-order phase transition at low temperatures, and an order -to-disorder transition at higher temperatures. This behavior resemble s that of some Langevin equations with multiplicative noise, which exh ibit also two analogous phase transitions as the noise amplitude is in creased. By comparing the standard models fur noise-induced transition s with our new Langevin equation we elucidate that the mechanisms cont rolling the disorder-to-order transitions in both of them are essentia lly different, even though fur both of them the presence of multiplica tive noise is a key ingredient. [S1063-651X(98)06911-6].