Sharp crossover and anomalously large correlation length in driven systems

TL;DR

This paper explains how driven diffusive systems can exhibit a sudden increase in correlation length due to a suppression of small domains, which can be mistaken for a phase transition.

Contribution

It introduces a simple mechanism within the driven diffusive systems and zero-range process framework to explain large correlation lengths without true phase transitions.

Findings

Large correlation lengths can arise from domain suppression.

The mechanism is demonstrated in two specific models.

The behavior mimics phase transition phenomena.

Abstract

Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase of the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behavior 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 length may build up. The mechanism is examined in detail in two models.