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The independence polynomial originates in statistical physics as thepartition function of the hard-core model. The location of the complex zeros ofthe polynomial is related to phase transitions, and plays an important role inthe design of efficient algorithms to approximately compute evaluations of thepolynomial.  In this paper we directly relate the location of the complex zeros of theindependence polynomial to computational hardness of approximating evaluationsof the independence polynomial. We do this by moreover relating the location ofzeros to chaotic behaviour of a naturally associated family of rationalfunctions; the occupation ratios.

Zeros, chaotic ratios and the computational complexity of approximating the independence polynomial