Journal of Statistical Physics, Vol. 123, No. 1, April 2006. p. 125-166.
DOI: 10.1007/s10955-006-9023-0
We present the Bethe ansatz solution for the discrete time zero range and asymmetric exclusion processes with fully parallel dynamics. The model depends on two parameters: p, the probability of single particle hopping, and q, the deformation parameter, which in the general case, |q| < 1, is responsible for long range interaction between particles...