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We consider a particle system on $Z^d$ with finite state space andinteractions of infinite range. Assuming that the rate of change is continuousand decays sufficiently fast, we introduce a perfect simulation algorithm forthe stationary process. The algorithm follows from a representation of themulticolor system as a finitary coding from a sequence of independent uniformrandom variables. This implies that the process is exponentially ergodic. Thebasic tool we use is a representation of the infinite range change rates as amixture of finite range change rates.

Perfect simulation and finitary coding for multicolor systems with interactions of infinite range