Exact Shock Profile for the ASEP with Sublattice-Parallel Update

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.

12 pages, 3 figures, accepted for publication in Journal of Physics A

References in corpus (8)

• Phase transitions in an exactly soluble one-dimensional exclusion process
• Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
• Shock Profiles for the Asymmetric Simple Exclusion Process in One Dimension
• The Lee-Yang theory of equilibrium and nonequilibrium phase transitions
• Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
• Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
• Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics
• Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics

Cited by in corpus (5)

• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Phase transitions in systems possessing Shock solutions
• Multi shocks in Reaction-diffusion models
• Matrix product solution for a partially asymmetric 1D lattice gas with a free defect
• Green functions for the TASEP with sublattice parallel update