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Paper IPM / P / 6763  


Abstract:  
We study a recently introduced model which consists of positive and negative particles on a ring. The positive (negative) particles hop clockwise (counterclockwise) with rate 1 and oppositely charged particles may swap their positions with asymmetric rates q and 1. In this paper we assume that a finite density of positively charged particles ρ and only one negative particle (which plays the role of an impurity) exist on the ring. It turns out that the canonical partition function of this model can be calculated exactly using Matrix Product Ansatz (MPA) formalism. In the limit of infinite system size and infinite number of positive particles, we can also derive exact expressions for the speed of the positive and negative particles which show a second order phase transition at q_{c}=2ρ. The density profile of the positive particles on the ring has a shock structure for q ≤ q_{c} and an exponential behaviour with correlation length ξ for q ≥ q_{c}. It will be shown that the meanfield results become exact at q=3 and no phase transition occurs for q > 2.
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