Construction of a matrix product stationary state from solutions of finite size system
چکیده
Stationary states of stochastic models, which have N states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite M -dimensional matrix product state for any {N,M}. Second, we give a method to construct the matrices from the stationary states of small size system when the above condition and N ≤ M are satisfied. Third, the method by which one can check that the obtained matrices are valid for any system size is presented for the case where M = N is satisfied. The application of our methods is explained using three examples: the asymmetric exclusion process, a model studied in [Jafarpour F H 2003 J. Phys. A: Math. Gen.36 7497] and a hybrid of both of the models.