  We study zeros of the partition functions of ferromagnetic 2-state spin
systems in terms of the external field, and obtain new zero-free regions of
these systems via a refinement of Asano's and Ruelle's contraction method. The
strength of our results is that they do not depend on the maximum degree of the
underlying graph. Via Barvinok's method, we also obtain new efficient and
deterministic approximate counting algorithms. In certain regimes, our
algorithm outperforms all other methods such as Markov chain Monte Carlo and
correlation decay.
