Given a countable set of sites and a collection of flip rates at each site,
we give a sufficient condition on the long-range dependancies of the flip rates
ensuring the well-definedness of the corresponding spin system. This hypothesis
has already been widely used since the interacting particle systems were
introduced, but our construction brings a new insight to understand why it is
natural. The process is first constructed as a limit of finite spin systems.
Then we identify its generator and give a simple criterion for a measure to be
invariant with respect to it.Comment: 12 page