Exact finite-size corrections in the dimer model on a cylinder
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917948192456704 |
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| author | Papoyan, Vladimir V. |
| author_facet | Papoyan, Vladimir V. |
| contents | The exact finite-size corrections to the free energy $F$ of the dimer model on lattice $\mathcal{M} \times \mathcal{N}$ with cylindrical boundary conditions have been derived for three cases where the lattice is completely covered by dimers: $\mathcal{M} = 2M$, $\mathcal{N} = 2N$; $\mathcal{M} = 2M - 1$, $\mathcal{N} = 2N$; and $\mathcal{M} = 2M$, $\mathcal{N} = 2N - 1$. For these types of cylinders, ratios $r_p(ρ)$ of the $p$th coefficient of $F$ have been calculated for the infinitely long cylinder (${\mathcal M} \rightarrow \infty$) and infinitely long strip (${\mathcal N} \rightarrow \infty$) at varying aspect ratios. As in previous studies of the dimer model on the rectangular lattice with free boundary conditions and for the Ising model with Brascamp-Kunz boundary conditions, the limiting values $p \to \infty$ exhibit abrupt anomalous behaviour of ratios $r_p(ρ)$ at certain values of $ρ$. These critical values of $ρ$ and the limiting values of the finite-size expansion coefficient ratios vary between the different models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact finite-size corrections in the dimer model on a cylinder Papoyan, Vladimir V. Statistical Mechanics The exact finite-size corrections to the free energy $F$ of the dimer model on lattice $\mathcal{M} \times \mathcal{N}$ with cylindrical boundary conditions have been derived for three cases where the lattice is completely covered by dimers: $\mathcal{M} = 2M$, $\mathcal{N} = 2N$; $\mathcal{M} = 2M - 1$, $\mathcal{N} = 2N$; and $\mathcal{M} = 2M$, $\mathcal{N} = 2N - 1$. For these types of cylinders, ratios $r_p(ρ)$ of the $p$th coefficient of $F$ have been calculated for the infinitely long cylinder (${\mathcal M} \rightarrow \infty$) and infinitely long strip (${\mathcal N} \rightarrow \infty$) at varying aspect ratios. As in previous studies of the dimer model on the rectangular lattice with free boundary conditions and for the Ising model with Brascamp-Kunz boundary conditions, the limiting values $p \to \infty$ exhibit abrupt anomalous behaviour of ratios $r_p(ρ)$ at certain values of $ρ$. These critical values of $ρ$ and the limiting values of the finite-size expansion coefficient ratios vary between the different models. |
| title | Exact finite-size corrections in the dimer model on a cylinder |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2407.19255 |