  We prove that a Gibbs point process interacting via a finite-range, repulsive
potential $\phi$ exhibits a strong spatial mixing property for activities
$\lambda < e/\Delta_{\phi}$, where $\Delta_{\phi}$ is the potential-weighted
connective constant of $\phi$, defined recently in [MP21]. Using this we derive
several analytic and algorithmic consequences when $\lambda$ satisfies this
bound: (1) We prove new identities for the infinite volume pressure and surface
pressure of such a process (and in the case of the surface pressure establish
its existence). (2) We prove that local block dynamics for sampling from the
model on a box of volume $N$ in $\mathbb R^d$ mixes in time $O(N \log N)$,
giving efficient randomized algorithms to approximate the partition function
and approximately sample from these models. (3) We use the above identities and
algorithms to give efficient approximation algorithms for the pressure and
surface pressure.
