A numerical study of the zeros of the grand partition function of $k$-mers on strips of width $k$

Abstract

We study numerically, the distribution of the zeros of the grand partition function of $k$-mers on a $k\times L$ strip in the complex activity (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.

10 + 3 pages, 13 figures. Typos and structuring fixed in v4

References in corpus (1)

• Hard hexagon partition function for complex fugacity