  We investigate unbounded continuous spin-systems with infinite-range
interactions. We develop a new technique for deducing decay of correlations
from a uniform Poincar\'e inequality based on a directional Poincar\'e
inequality, which we derive through an averaging procedure. We show that this
decay of correlations is equivalent to the Dobrushin-Shlosman mixing condition.
With this, we also state and provide a partial answer to a conjecture regarding
the relationship between the relaxation rates of non-ferromagnetic and
ferromagnetic systems. Finally, we show that for a symmetric, ferromagnetic
system with zero boundary conditions, a weaker decay of correlations can be
bootstrapped.
