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 $Δ$. This new domain contains the half disk $$D=\left\{ λ\in \mathbb{C}\ |\ \mathrm{Re}(λ)\geq 0, |λ|\leq \frac{7}{8}\tan \left( \fracπ{2(Δ-1)}\right)\right\}.$$
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