Entropy of full covering of the kagome lattice by straight trimers
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915688225964032 |
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| author | Dhar, Deepak Oliveira, Tiago J. Rajesh, R. Stilck, Jürgen F. |
| author_facet | Dhar, Deepak Oliveira, Tiago J. Rajesh, R. Stilck, Jürgen F. |
| contents | We consider the number of ways all the sites of a kagome lattice can be covered by non-overlapping linear rigid rods where each rod covers 3 sites. We establish a 2-to-1 correspondence between the configurations of trimers on the kagome lattice to the covering by dimers of a related hexagonal lattice to show that entropy of coverings per trimer $s_{\text{tri,kag}}$ equals the entropy per dimer $ s_{\text{dim,hex}} $, and is given by $ s_{\text{tri,kag}} = s_{\text{dim,hex}} = \frac{1}{2 π} \int_0^{ 2 π/3} \log( 2 + 2 \cos k) dk \approx 0.323065947\ldots$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropy of full covering of the kagome lattice by straight trimers Dhar, Deepak Oliveira, Tiago J. Rajesh, R. Stilck, Jürgen F. Statistical Mechanics We consider the number of ways all the sites of a kagome lattice can be covered by non-overlapping linear rigid rods where each rod covers 3 sites. We establish a 2-to-1 correspondence between the configurations of trimers on the kagome lattice to the covering by dimers of a related hexagonal lattice to show that entropy of coverings per trimer $s_{\text{tri,kag}}$ equals the entropy per dimer $ s_{\text{dim,hex}} $, and is given by $ s_{\text{tri,kag}} = s_{\text{dim,hex}} = \frac{1}{2 π} \int_0^{ 2 π/3} \log( 2 + 2 \cos k) dk \approx 0.323065947\ldots$. |
| title | Entropy of full covering of the kagome lattice by straight trimers |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.18307 |