Exact simulation for discrete time spin systems and unilateral fields

In this paper we generalize the technique presented by Haggstrom and Steif (Comb. Probab. Comput. 9:425-439, 2000) for the exact simulation of finite sections of infinite-volume Gibbs random fields, to a more general class of discrete time nearest neighbour spin systems. The main role is played by an auxiliary binary field, which indicates the sampling region. Percolation bounds can be used to prove that the algorithm terminates a.s. In the simplest case this field is Bernoulli; however blocking techniques can be used that destroy the independence property but extend the validity of the algorithm. Finally, the connection with stationary unilateral fields in the plane considered by Pickard (Adv. Appl. Probab. 12:655-671, 1980) and Galbraith and Walley (J. Appl. Probab. 19:332-343, 1982) is discussed.