Phase Transitions and Even/Odd Effects in Asymmetric Exclusion Models

Summary

An asymmetric exclusion process with periodic boundary conditions is investigated. During each time-step a randomly chosen particle moves one site and if possible two sites. This dynamics leads to different gap distributions depending on the parity of the number of holes. Despite the simplicity of the model on a ring there is a phase transition that separates two regimes with different density profiles. For a generalization of the process the steady state is given for two particles on a ring.