Note on the zero-free region of the hard-core model

Abstract

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 $$D=\left\{\lambda \in \mathbb{C}|\mathrm{Re}(\lambda )\ge 0,|\lambda |\le \frac{7}{8}\tan \left(\frac{\pi }{2(\Delta -1)}\right)\right\}.$$

7 pages, 1 figure