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Physica A Statistical Mechanics and its Applications

How fractal defects can affect critical phenomena?

Xiaoping Wu, Wei Zhong

Published Mar 17, 2025• 0 citations
Publisher
DOI
10.1016/j.physa.2025.130531

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The critical behavior of the classical Ising model on a three-dimensional fractal lattice with Hausdorff dimension dH=ln⁡32/ln⁡4=2.5d_H = \ln32 / \ln4 = 2.5dH​=ln32/ln4=2.5 is investigated using the higher-order tensor renormalization group (HOTRG) method. We determine the critical temperature Tc≈2.65231T_c \approx 2.65231Tc​≈2.65231 and the critical exponents for magnetization β≈0.059β\approx 0.059β≈0.059 and field response δ≈35δ\approx 35δ≈35. Unlike a previously studied 2D fractal with dH≈1.792d_H \approx 1.792dH​≈1.792, the specific heat for this 3D fractal exhibits a divergent singularity at TcT_cTc​. The results are compared with those for regular lattices and other fractal structures to elucidate the role of dimensionality in critical phenomena.