Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912451267657728 |
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| author | Genzor, Jozef Krčmár, Roman Ueda, Hiroshi Kochan, Denis Gendiar, Andrej Nishino, Tomotoshi |
| author_facet | Genzor, Jozef Krčmár, Roman Ueda, Hiroshi Kochan, Denis Gendiar, Andrej Nishino, Tomotoshi |
| contents | The critical behavior of the classical Ising model on a three-dimensional fractal lattice with Hausdorff dimension $d_H = \ln32 / \ln4 = 2.5$ is investigated using the higher-order tensor renormalization group (HOTRG) method. We determine the critical temperature $T_c \approx 2.65231$ and the critical exponents for magnetization $β\approx 0.059$ and field response $δ\approx 35$. Unlike a previously studied 2D fractal with $d_H \approx 1.792$, the specific heat for this 3D fractal exhibits a divergent singularity at $T_c$. The results are compared with those for regular lattices and other fractal structures to elucidate the role of dimensionality in critical phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice Genzor, Jozef Krčmár, Roman Ueda, Hiroshi Kochan, Denis Gendiar, Andrej Nishino, Tomotoshi Statistical Mechanics The critical behavior of the classical Ising model on a three-dimensional fractal lattice with Hausdorff dimension $d_H = \ln32 / \ln4 = 2.5$ is investigated using the higher-order tensor renormalization group (HOTRG) method. We determine the critical temperature $T_c \approx 2.65231$ and the critical exponents for magnetization $β\approx 0.059$ and field response $δ\approx 35$. Unlike a previously studied 2D fractal with $d_H \approx 1.792$, the specific heat for this 3D fractal exhibits a divergent singularity at $T_c$. The results are compared with those for regular lattices and other fractal structures to elucidate the role of dimensionality in critical phenomena. |
| title | Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2506.17053 |