Absence of phase coexistence in disordered exclusion processes with bypassing

TL;DR

This study investigates how bypassing defect sites in disordered exclusion processes affects phase coexistence, revealing that such coexistence can be absent in finite systems but appears in the thermodynamic limit.

Contribution

The paper introduces models allowing particles to bypass defects and demonstrates conditions under which phase coexistence is suppressed or present.

Findings

Phase coexistence may be absent in finite systems with bypassing

Phase coexistence reappears in the thermodynamic limit for certain models

Anisotropic lattice models can exhibit regimes without phase coexistence

Abstract

Adding quenched disorder to the one-dimensional asymmetric exclusion process is known to always induce phase separation. To test the robustness of this result, we introduce two modifications of the process that allow particles to bypass defect sites. In the first case, particles are allowed to jump l sites ahead with the probability p_l ~ l^-(1+sigma), where sigma>1. By using Monte Carlo simulations and the mean-field approach, we show that phase 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 totally asymmetric hopping perpendicular to and along the direction of driving, respectively. We show that in an anisotropic limit of this model a regime may be found where phase coexistence is absent.