Before revision:  We apply the method of polynomial interpolation, for which we prove that \sum_x e^{ f \tilde{f} (x)} \ne 0 for complex a _{ij and b_i such that \sum_j |\Re} a _{ij| \leq 1-\delta, \sum_j |\Im} a_{ij| \leq \delta^2/10 and |\Im} b_i| \leq \delta^2/10 for all i, which is\tilde{f}  interpreted as the absence of a phase transition in the Lee - Yang sense in the corresponding Ising model.
After revision:  We apply the method of polynomial interpolation, for which we prove that \sum_x e^{ f \tilde{f} (x)} \ne 0 for complex a _{ij and b_i such that \sum_j |\Re} a _{ij| \leq 1-\delta, \sum_j |\Im} a_{ij| \leq \delta^2/10 and |\Im} b_i| \leq \delta^2/10 for all i, which is\tilde{f} in a neighborhood of a real-valued f satisfying the above mentioned conditions. The bounds are asymptotically optimal. Results on the zero-free region are interpreted as the absence of a phase transition in the Lee - Yang sense in the corresponding Ising model.