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

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Abstract
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 was claimed that the spatial particle condensation the model exhibits is not associated with a phase transition in the framework of a grand canonical ensemble. The discussions were, however, based on an assumption about the monotonicity of a certain function appearing in the analysis. In this paper we prove the assertion. The proof combined with the previous discussions shows convincingly that there is no phase transition in the framework of a grand canonical ensemble.