Sharp crossover and anomalously large correlation length in driven systems

Models of one-dimensional driven diffusive systems sometimes exhibit. an abrupt increase in the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behaviour may be misinterpreted as a genuine phase transition. A simple mechanism for this sharp increase is presented. The mechanism is introduced within the framework of a recently suggested correspondence between driven diffusive systems and zero-range processes. It is shown that when the dynamics of the model is such that small domains are suppressed in the steady-state distribution, anomalously large correlation lengths may build up. The mechanism is examined in detail in two models.