Quantum phase transition in transverse-field Ising model on Sierpiński gasket lattice

• URL: http://arxiv.org/abs/2602.02904v1
• Date: Mon, 02 Feb 2026 23:20:00 GMT
• Title: Quantum phase transition in transverse-field Ising model on Sierpiński gasket lattice
• Authors: Tymoteusz Braciszewski, Oliwier Urbański, Piotr Tomczak,
• Abstract summary: We study quantum phase transition in the transverse-field Ising model on the Sierpiski gasket.<n>By applying finite-size scaling and numerical renormalization group methods, we determine the critical coupling and the exponents that describe this transition.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study quantum phase transition in the transverse-field Ising model on the Sierpiński gasket. By applying finite-size scaling and numerical renormalization group methods, we determine the critical coupling and the exponents that describe this transition. We first checked our finite-size scaling and the renormalization methods on the exactly solvable one-dimensional chain, where we recovered proper values of critical couplings and exponents. Then, we applied the method to the Sierpiński gasket with 11 and 15 spins. We found a quantum critical point at $λ_c \approx 2.72$ to $2.93$, with critical exponents $z\approx0.84$, $ν\approx 1.12 $, $β\approx 0.30$, and $γ\approx 2.54$. The lower dynamical exponent $z$ indicates that quantum fluctuations slow down due to fractal geometry, yielding an effective critical dimension of about 2.43. The numerical renormalization group method yielded similar results $λ_c = 2.765$, $β= 0.306$, supporting our findings. These exponents differ from those in both the one-dimensional and mean-field cases.

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