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Phase transitions in the asymmetric exclusion process with long-range hopping

We study the exclusion process in which particles may jump any distance l with the probability that decays as l^(-1-\sigma). Besides the localization of the domain-wall at first-order phase transition, previous results [J. Szavits-Nossan and K. Uzelac, Phys. Rev. E 74, 051104 (2006)] have shown a change in the continuous phase transition to the maximum-current phase. In particular, the exponent of the algebraic decay of the density profile differs from the short-range value 1/2 in the region 1<\sigma<2, where its dependence on \sigma was given by the conjecture based on numerical simulations. In the present work, we obtain the exact value of this exponent from a hydrodynamic equation for the density profile in the mean-field approximation [J. Szavits-Nossan and K. Uzelac, Phys. Rev. E 77, 051116 (2008)]. For \sigma>2, this equation is given by the viscous Burgers equation of the short-range case, but the usual diffusion term of this equation is replaced by the fractional one for 1<\sigma<2. In case of the translationally invariant system, the equation can be mapped onto the fractional Kardar-Parisi-Zhang equation [E. Katzav, Phys. Rev. E 68, 031607 (2003)] which predicts the value of the dynamical exponent z=min{; ; \sigma, 3/2}; ; , in agreement with the results of our numerical simulations on the half-filled chain with periodic boundary conditions.

exclusion process; phase transitons; out-of-equilibrium; long-range interactions

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