Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We consider a particle system on Z(d) with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture of finite range change rates. Furthermore, if a high noise condition holds, as an application of this decomposition, we design a feasible perfect simulation algorithm to sample from the stationary process. Finally, the perfect simulation scheme allows us to forge an algorithm to obtain an explicit construction of a coupling attaining Ornstein's (d) over bar -distance for two ordered Ising probability measures.23416291659Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)[ANR-08-BLAN-0220-01][Prin07: 20078XYHYS]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [305447/2008-4, 302755/2010-1][ANR-08-BLAN-0220-01][Prin07: 20078XYHYS]