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We study complex zeros of the partition function of 2-spin systems, viewed asa multivariate polynomial in terms of the edge interaction parameters and theuniform external field. We obtain new zero-free regions in which all theseparameters are complex-valued. Crucially based on the zero-freeness, we showthe existence of correlation decay in these regions. As a consequence, weobtain an FPTAS for computing the partition function of 2-spin systems ongraphs of bounded degree for these parameter settings. We introduce thecontraction property as a unified sufficient condition to devise FPTAS viaeither Weitz's algorithm or Barvinok's algorithm. Our main technicalcontribution is a very simple but general approach to extend any real parameterof which the 2-spin system exhibits correlation decay to its complexneighborhood where the partition function is zero-free and correlation decaystill exists. This result formally establishes the inherent connection betweentwo distinct notions of phase transition for 2-spin systems: the existence ofcorrelation decay and the zero-freeness of the partition function via a unifiedperspective, contraction.

Contraction: a Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems