title: Phase transitions in systems possessing shock solutions.
abstract: Recently it has been shown that there are three families of stochastic one-dimensional nonequilibrium lattice models for which the single-shock measures form an invariant subspace of the states of these models. Here, both the stationary states and dynamics of single-shocks on a one-dimensional lattice are studied. This is done for both an infinite lattice and a finite lattice with boundaries. It is seen that these models possess both static and dynamical phase transitions. The static phase transition is the well-known low-high density phase transition for the asymmetric simple exclusion process. The branching-coalescing random walk and asymmetric Kawasaki-Glauber process models also show the same phase transition. Double-shocks on a one-dimensional lattice are also investigated. It is shown that at the stationary state the contribution of double-shocks with higher width becomes small, and the main contribution comes from thin double-shocks.
authors.affiliation: Department of Physics, Alzahra University, Tehran 19938-91167, Iran. m_arabsalmani@alzahra.ac.ir
authors.forename: Maryam
authors.initials: M
authors.lastname: Arabsalmani
authors.forename: Amir
authors.initials: A
authors.lastname: Aghamohammadi