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We study boundedness of zeros of the independence polynomial of tori forsequences of tori converging to the integer lattice. We prove that zeros arebounded for sequences of balanced tori, but unbounded for sequences of highlyunbalanced tori. Here balanced means that the size of the torus is at mostexponential in the shortest side length, while highly unbalanced means that thelongest side length of the torus is super exponential in the product over theother side lengths cubed. We discuss implications of our results to theexistence of efficient algorithms for approximating the independence polynomialon tori.

On boundedness of zeros of the independence polynomial of tori