Ising model on the aperiodic Smith hat
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915183464546304 |
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| author | Okabe, Yutaka Niizeki, Komajiro Araki, Yoshiaki |
| author_facet | Okabe, Yutaka Niizeki, Komajiro Araki, Yoshiaki |
| contents | Smith et al discovered an aperiodic monotile of 13-sided shape in 2023. It is called the `Smith hat' and consists of 8 kites. We deal with the statistical physics of the lattice of the kites, which we call the `Smith-kite lattice'. We studied the Ising model on the aperiodic Smith-kite lattice and the dual Smith-kite lattice using Monte Carlo simulations. We combined the Swendsen-Wang multi-cluster algorithm and the replica exchange method. We simulated systems up to the total spin number $939201$. Using the finite-size scaling analysis, we estimated the critical temperature on the Smith-kite lattice as $T_c/J=2.405 \pm 0.0005$ and that of the dual Smith-kite lattice as $T^{*}_{c}/J=2.143 \pm 0.0005$. Moreover, we confirmed the duality relation between the critical temperatures on the dual pair of aperiodic lattices, $\sinh(2J/T_c) \sinh(2J/T^{*}_{c}) = 1.000 \pm 0.001$. We also checked the duality relation for the nearest-neighbor correlation at the critical temperature, essentially the energy, $ε(T_c)/\coth(2J/T_c) + ε(T^{*}_c)/\coth(2J/T^{*}_c) = 1.000 \pm 0.001$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ising model on the aperiodic Smith hat Okabe, Yutaka Niizeki, Komajiro Araki, Yoshiaki Statistical Mechanics Smith et al discovered an aperiodic monotile of 13-sided shape in 2023. It is called the `Smith hat' and consists of 8 kites. We deal with the statistical physics of the lattice of the kites, which we call the `Smith-kite lattice'. We studied the Ising model on the aperiodic Smith-kite lattice and the dual Smith-kite lattice using Monte Carlo simulations. We combined the Swendsen-Wang multi-cluster algorithm and the replica exchange method. We simulated systems up to the total spin number $939201$. Using the finite-size scaling analysis, we estimated the critical temperature on the Smith-kite lattice as $T_c/J=2.405 \pm 0.0005$ and that of the dual Smith-kite lattice as $T^{*}_{c}/J=2.143 \pm 0.0005$. Moreover, we confirmed the duality relation between the critical temperatures on the dual pair of aperiodic lattices, $\sinh(2J/T_c) \sinh(2J/T^{*}_{c}) = 1.000 \pm 0.001$. We also checked the duality relation for the nearest-neighbor correlation at the critical temperature, essentially the energy, $ε(T_c)/\coth(2J/T_c) + ε(T^{*}_c)/\coth(2J/T^{*}_c) = 1.000 \pm 0.001$. |
| title | Ising model on the aperiodic Smith hat |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2402.11331 |