Exact Shock Profile for the ASEP with Sublattice-Parallel Update

TL;DR

This paper provides an exact analytical solution for the stationary states and phase transitions of the ASEP with sublattice-parallel update, confirming previous numerical findings and revealing two second-order phase transitions.

Contribution

It introduces an exact matrix product solution for the ASEP with sublattice-parallel update and characterizes its phase transitions.

Findings

Identifies three distinct phases in the model.

Calculates exact density profiles for each phase.

Discovers two second-order phase transitions.

Abstract

We analytically study the one-dimensional Asymmetric Simple Exclusion Process (ASEP) with open boundaries under sublattice-parallel updating scheme. We investigate the stationary state properties of this model conditioned on finding a given particle number in the system. Recent numerical investigations have shown that the model possesses three different phases in this case. Using a matrix product method we calculate both exact canonical partition function and also density profiles of the particles in each phase. Application of the Yang-Lee theory reveals that the model undergoes two second-order phase transitions at critical points. These results confirm the correctness of our previous numerical studies.