In statistical physics, the zero-freeness property of the grand canonical partition function guarantees the analyticity of the pressure as we approach the infinite volume limit, as shown by Lee and Yang in 1952. Moreover, computer scientists have leveraged the zero-freeness property of the grand canonical partition function to approximate it using various algorithms, such as Barvinok's algorithm. We introduce a novel approach, rooted in computer science, known as the recursion method. This method gives a zero-free region of the partition function. Specifically, we investigate the application of this method to the hard-core lattice gas model, following the work by Peters and Regts in 2019. Additionally, we briefly discuss how Michelen and Perkins (2023) adapted this method for studying gas particles in a continuum space, which interact via a repulsive potential.