  We consider a particle system on $\mathbb{Z}^d$ 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 $\bar{d}$-distance for two
ordered Ising probability measures.
