A numerical study of the zeros of the grand partition function of k-mers on strips of width k
Year: 2025
Type: article
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.
Author: Soumyadeep Sarma
Institution: Indian Institute of Science Bangalore
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409232276