  In this paper we prove a new zero-free region for the partition function of
the hard-core model, that is, the independence polynomials of graphs with
largest degree $\Delta$. This new domain contains the half disk $$D=\left\{
\lambda \in \mathbb{C}\ |\ \mathrm{Re}(\lambda)\geq 0, |\lambda|\leq
\frac{7}{8}\tan \left( \frac{\pi}{2(\Delta-1)}\right)\right\}.$$
