A numerical study of the zeros of the grand partition function of <i>k</i>-mers on strips of width <i>k</i>

Abstract We study numerically, the distribution of the zeros of the grand partition function of k -mers on a k × L strip in the complex fugacity ( z ) plane. Using transfer matrix methods, we find that our results match the analytical predictions of Heilmann and Leib for k = 2. However, for k = 3, the zeros are confined within a bounded region, suggesting a fundamental difference in critical behavior. This indicates that trimers belong to a distinct universality class in some finite geometries. We observe that the density of zeros along multiple line segments in the complex plane reveals a richer structure than in the dimer case. Our findings emphasize the role of geometric constraints in shaping the statistical mechanics of k -mer models and set the stage for further studies in higher-dimensional lattices.