On the existence of a phase transition for an exclusion process on a ring

We study the stationary state of a simple exclusion process on a ring which was introduced by Arndt et al. In a previous study by Rajewsky et al it wa s claimed that the spatial particle condensation the model exhibits is not associated with a phase transition in the framework of a grand canonical en semble. The discussions were, however, based on an assumption about the mon otonicity of a certain function appearing in the analysis. In this paper we prove the assertion. The proof combined with the previous discussions show s convincingly that there is no phase transition in the framework of a gran d canonical ensemble.