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.

翻译：我们研究当环面序列收敛到整数格点时，其独立多项式零点的有界性。我们证明：对于平衡环面序列，零点是有界的；而对于高度非平衡环面序列，零点则无界。其中"平衡"指环面尺寸至多随最短边长的指数增长，而"高度非平衡"指环面最长边长相对于其他边长乘积的立方呈超指数增长。我们讨论了该结果对环面上独立多项式近似计算的高效算法存在性问题的启示。