Critical temperature(s) of Sierpiński carpet(s)
Year: 2026
Authors: Zinati RB., Gori G., Codello A.
Autors Affiliation: Univ Svizzera Italiana, CH-6900 Lugano, Switzerland; CNR INO, Area Sci Pk, I-34149 Trieste, Italy; Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; Ca Foscari Univ Venice, DMSN, Via Torino 155, I-30172 Venice, Italy; Univ Republica, IFFI, JHy Reissig 565, Montevideo 11300, Uruguay.
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 SCk(a,b), 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 k=10 for the canonical SCk(3,1) carpet. Extrapolation from these data yields the most accurate estimate to date of the critical temperature Tc(3,1)=1.4782927(26). We further extend the analysis to additional members of the SCk(a,b) family and report their corresponding critical temperatures.
Journal/Review: EUROPEAN PHYSICAL JOURNAL B
Volume: 99 (6) Pages from: 82-1 to: 82-7
More Information: Open access funding provided by Universita della Svizzera italiana.KeyWords: Ising-model; FractalsDOI: 10.1140/epjb/s10051-026-01196-1
