Absence of phase coexistence in disordered exclusion processes with bypassing

Abstract

Adding quenched disorder to the one-dimensional asymmetric exclusionprocess is known to always induce phase separation. To test the robustnessof this result, we introduce two modifications of the process that allowparticles to bypass defect sites. In the first case, particles are allowed to jumpl sites ahead withthe probability pl ∼ l − (1 + σ), where σ > 1. By using Monte Carlo simulations and the mean-field approach, we show thatphase coexistence may be absent up to enormously large system sizes, e.g. lnL ∼ 50, but is present in the thermodynamic limit, as in the short-range case. In the second case,we consider the exclusion process on a quadratic lattice with symmetric and totallyasymmetric hopping perpendicular to and along the direction of driving, respectively. Weshow that in an anisotropic limit of this model a regime may be found where phasecoexistence is absent.