Spatial particle condensation for an exclusion process on a ring

We study the stationary state of a simple exclusion process on a ring which was recently introduced by Arndt et al. (J. Phys. A 31 (1998) L45; J. Stat . Phys. 97 (1999) 1). This model exhibits spatial condensation of particles . It has been argued (J. Phys. A 31 (1998) L45; condmat/9809123) that the m odel has a phase transition from a "mixed phase" to a "disordered phase". H owever, in this paper exact calculations are presented which, we believe, s how that in the framework of a grand canonical ensemble there is no such ph ase transition. An analysis of the fluctuations in the particle density str ongly suggests that the same result also holds for the canonical ensemble a nd suggests the existence of extremely long (but finite) correlation length s (for example 10(70) sites) in the infinite system at moderate parameter v alues in the mixed regime. (C) 2000 Elsevier Science B.V. All rights reserv ed.