  We study boundedness of zeros of the independence polynomial of tori for
sequences of tori converging to the integer lattice. We prove that zeros are
bounded for sequences of balanced tori, but unbounded for sequences of highly
unbalanced tori. Here balanced means that the size of the torus is at most
exponential in the shortest side length, while highly unbalanced means that the
longest side length of the torus is super exponential in the product over the
other side lengths cubed. We discuss implications of our results to the
existence of efficient algorithms for approximating the independence polynomial
on tori.
