Numerical study of phase transition in an exclusion model with parallel dynamics

A numerical method based on matrix product formalism is proposed to study the phase transitions and shock formation in the asymmetric simple exclusion process with open boundaries and parallel dynamics. By working in a canonical ensemble, where the total number of the particles is being fixed, we find that the model has a rather non-trivial phase diagram consisting of three different phases which are separated by second-order phase transition. Shocks may evolve in the system for special values of the reaction parameters