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

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

paper

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

arXiv:2506.17053

Abstract

The critical behavior of the classical Ising model on a three-dimensional fractal lattice with Hausdorff dimension $d_{H} = ln 32/ ln 4 = 2.5$ 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.

7 pages, 5 figures, 2 tables