https://doi.org/10.1140/epjb/s10051-026-01196-1
Research – Statistical and Nonlinear Physics
Critical temperature(s) of Sierpiński carpet(s)
1
Università della Svizzera italiana, 6900, Lugano, Switzerland
2
CNR-INO, Area Science Park, 34149, Basovizza, Trieste, Italy
3
Institut für Theoretische Physik, Universität Heidelberg, 69120, Heidelberg, Germany
4
DMSN, Ca’ Foscari University of Venice, Via Torino 155, 30172, Venice, Italy
5
IFFI, Universidad de la República, J.H.y Reissig 565, 11300, Montevideo, Uruguay
a
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Received:
24
March
2026
Accepted:
29
May
2026
Published online:
23
June
2026
Abstract
We present a key algorithmic improvement to the generalized combinatorial Feynman–Vdovichenko method for calculating the critical temperature of the Ising model on Sierpiński carpets 
, originally introduced in arxiv:1505.02699. By reformulating the method in terms of purely real-valued transition matrices, we substantially reduce their dimension. This optimization, together with modern computational resources, enables us to reach generation 
for the canonical 
carpet. Extrapolation from these data yields the most accurate estimate to date of the critical temperature 
. We further extend the analysis to additional members of the family and report their corresponding critical temperatures.
© The Author(s) 2026
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