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Paper   IPM / Physic / 6763
School of Physics
  Title:   Exact Solution of An Exclusion Model in the Presence of A Moving Impurity on A Ring
  Author(s):  F. Jafarpour
  Status:   Published
  Journal: J. Phys. A: Math. Gen.
  No.:  28
  Vol.:  33
  Year:  2000
  Pages:   8673-8680
  Supported by:  IPM
  Abstract:
We study a recently introduced model which consists of positive and negative particles on a ring. The positive (negative) particles hop clockwise (counter-clockwise) 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 qc=2ρ. The density profile of the positive particles on the ring has a shock structure for qqc and an exponential behaviour with correlation length ξ for qqc. It will be shown that the mean-field results become exact at q=3 and no phase transition occurs for q > 2.

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