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# Title:Measurements of magnetization on the Sierpiński carpet

Abstract: Phase transition of the classical Ising model on the Sierpiński carpet, which has the fractal dimension $\log_3^{~} 8 \approx 1.8927$, is studied by an adapted variant of the higher-order tensor renormalization group method. The second-order phase transition is observed at the critical temperature $T_{\rm c}^{~} = 1.4783(1)$. Position dependence of local functions is studied by means of impurity tensors, which are inserted at different locations on the fractal lattice. The critical exponent $\beta$ associated with the local magnetization varies by two orders of magnitude, depending on lattice locations, whereas $T_{\rm c}^{~}$ is not affected.
 Comments: 7 pages, 10 figs Subjects: Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:1904.10645 [cond-mat.stat-mech] (or arXiv:1904.10645v1 [cond-mat.stat-mech] for this version)

## Submission history

From: Andrej Gendiar [view email]
[v1] Wed, 24 Apr 2019 05:22:45 UTC (498 KB)
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