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Abstract
We consider the totally asymmetric simple exclusion process (TASEP) on the periodic
chain in the presence of a single impurity site that is inaccessible to other particles
and therefore acts as a static defect. Particles are allowed to advance any distance
l \geq 1 on the right with the probability that decays as l^-(1+sigma), where sigma
> 1. Despite the long range of hopping, we find the same type of phase transition
that occurs in the standard short-range TASEP with a defect site where defect induces
a macroscopic shock in the stationary state. In particular, our model displays two
main features characteristic of the short-range TASEP with defect site: a growth of
the shock width with system size L as L^(1/2) or L^(1/3), depending on the existence
of the particle-hole symmetry, and the power-law decay in density profiles of the
shock phase. However, unlike the profiles in the short-range case, we find that the
latter are well reproduced by the mean-field approximation, which enables us to derive
the analytical expression for sigma-dependent exponent nu = sigma-1 of this power-law
decay and the point sigma_c = 4/3 at which the transition takes place.