  We prove that for every locally stable and tempered pair potential $\phi$
with bounded range, there exists a unique infinite-volume Gibbs point process
on $\mathbb{R}^d$ for every activity $\lambda < (e^{L} \hat{C}_{\phi})^{-1}$,
where $L$ is the local stability constant and $\hat{C}_{\phi}:= \mathrm{sup}_{x
\in \mathbb{R}^{d}} \int_{\mathbb{R}^{d}} 1 - e^{-|\phi(x, y)|} dy$ is the
(weak) temperedness constant. Our result extends the uniqueness regime that is
given by the classical Ruelle--Penrose bound by a factor of at least $e$, where
the improvements becomes larger as the negative parts of the potential become
more prominent (i.e., for attractive interactions at low temperature). Our
technique is based on the approach of Dyer et al. (Rand. Struct. & Alg. '04):
we show that for any bounded region and any boundary condition, we can
construct a Markov process (in our case spatial birth-death dynamics) that
converges rapidly to the finite-volume Gibbs point process while effects of the
boundary condition propagate sufficiently slowly. As a result, we obtain a
spatial mixing property that implies uniqueness of the infinite-volume Gibbs
measure.
