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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2409.07744 |
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| _version_ | 1866909580830703616 |
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| author | Sarma, Soumyadeep |
| author_facet | Sarma, Soumyadeep |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A numerical study of the zeros of the grand partition function of $k$-mers on strips of width $k$ Sarma, Soumyadeep Statistical Mechanics 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. |
| title | A numerical study of the zeros of the grand partition function of $k$-mers on strips of width $k$ |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2409.07744 |