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We study a recently introduced model which consists of positive and negativeparticles on a ring. The positive (negative) particles hop clockwise(counter-clockwise) with rate 1 and oppositely charged particles may swap theirpositions with asymmetric rates q and 1. In this paper we assume that a finitedensity of positively charged particles $\rho$ and only one negative particle(which plays the role of an impurity) exist on the ring. It turns out that thecanonical partition function of this model can be calculated exactly usingMatrix Product Ansatz (MPA) formalism. In the limit of infinite system size andinfinite number of positive particles, we can also derive exact expressions forthe speed of the positive and negative particles which show a second orderphase transition at $q_c=2\rho$. The density profile of the positive particleson the ring has a shock structure for $q \leq q_c$ and an exponential behaviourwith correlation length $\xi$ for $q \geq q_c$. It will be shown that themean-field results become exact at q=3 and no phase transition occurs for q>2.Comment: 9 pages,4 EPS figures. To be appear in JP

Exact solution of an exclusion model in the presence of a moving impurity on a ring