Critical Temperature(s) of Sierpinski Carpet(s)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915826795282432 |
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| author | Zinati, Riccardo Ben Alì Gori, Giacomo Codello, Alessandro |
| author_facet | Zinati, Riccardo Ben Alì Gori, Giacomo Codello, Alessandro |
| contents | We present a key algorithmic improvement to the generalized combinatorial Feynman--Vdovichenko method for calculating the critical temperature of the Ising model on Sierpinski carpets $SC_k(a,b)$, originally introduced in arxiv:1505.02699. By reformulating the method in terms of purely real-valued transfer matrices, we substantially reduce their dimension. This optimization, together with modern computational resources, enables us to reach generation $k=10$ for the canonical $SC_k(3,1)$ carpet. Extrapolation from these data yields the most accurate estimate to date of the critical temperature $T_c^{(3,1)} = 1.4782927(26)$. We further extend the analysis to additional members of the $SC_k(a,b)$ family and report their corresponding critical temperatures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_20295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical Temperature(s) of Sierpinski Carpet(s) Zinati, Riccardo Ben Alì Gori, Giacomo Codello, Alessandro Statistical Mechanics High Energy Physics - Lattice We present a key algorithmic improvement to the generalized combinatorial Feynman--Vdovichenko method for calculating the critical temperature of the Ising model on Sierpinski carpets $SC_k(a,b)$, originally introduced in arxiv:1505.02699. By reformulating the method in terms of purely real-valued transfer matrices, we substantially reduce their dimension. This optimization, together with modern computational resources, enables us to reach generation $k=10$ for the canonical $SC_k(3,1)$ carpet. Extrapolation from these data yields the most accurate estimate to date of the critical temperature $T_c^{(3,1)} = 1.4782927(26)$. We further extend the analysis to additional members of the $SC_k(a,b)$ family and report their corresponding critical temperatures. |
| title | Critical Temperature(s) of Sierpinski Carpet(s) |
| topic | Statistical Mechanics High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2512.20295 |