Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study

Abstract

We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpiński fractal with Hausdorff dimension $d_f\simeq 1.8928$. This method is shown to be relevant to the calculation of the critical temperature $T_c$ and the magnetic eigen-exponent $y_h$ on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigen-exponent $y_t$. At last, the results are shown to be consistent with a finite size scaling analysis.

arXiv comment16 pages, 7 figures

References in corpus (4)

• Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach
• Monte Carlo Renormalization of the 3-D Ising model: Analyticity and Convergence
• Critical Exponents of the 3-D Ising Model
• Critical behavior of the 3-state Potts model on Sierpinski carpet

Cited by in corpus (7)

• Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study
• The Ising model in planar lacunary and fractal lattices, a path counting approach
• J1-J2 fractal studied by multi-recursion tensor-network method
• Measurements of magnetization on the Sierpiński carpet
• Approximating the Ising model on fractal lattices of dimension below two
• Scaling law of Wolff cluster surface energy
• Critical Temperature(s) of Sierpinski Carpet(s)