  We consider the monomer-dimer model, whose realisations are spanning
sub-graphs of a given graph such that every vertex has degree zero or one. The
measure depends on a parameter, the monomer activity, which rewards the total
number of monomers. We consider general correlation functions including
monomer-monomer correlations and dimer-dimer covariances. We show that these
correlations decay exponentially fast with the distance if the monomer activity
is strictly positive. Our result improves a previous upper bound from van den
Berg and is of interest due to its relation to truncated spin-spin correlations
in classical spin systems. Our proof is based on the cluster expansion
technique.
