Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice

Jozef Genzor; Roman Krčmár; Hiroshi Ueda; Denis Kochan; Andrej Gendiar; Tomotoshi Nishino

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arXiv · 2506.17053

Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice

Jozef Genzor·Roman Krčmár·Hiroshi Ueda·Denis Kochan·Andrej Gendiar·Tomotoshi Nishino

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Abstract

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 $\beta \approx 0.059$ and field response $\delta \approx 35$. 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.

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Jozef Genzor, Roman Krčmár, Hiroshi Ueda, Denis Kochan, Andrej Gendiar, Tomotoshi Nishino. 2025-06-20. Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice. https://arxiv.org/abs/2506.17053

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