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

TL;DR

This study uses Monte Carlo Renormalization Group methods to analyze the critical behavior of the ferromagnetic Ising model on a Sierpinski carpet, providing insights into critical temperature and magnetic exponents on fractal structures.

Contribution

It demonstrates the effectiveness of Monte Carlo Renormalization Group analysis for studying phase transitions on fractal lattices, specifically calculating critical temperature and magnetic eigen-exponent.

Findings

Critical temperature $T_c$ and magnetic eigen-exponent $y_h$ were successfully estimated.

Scaling corrections affected the calculation of the temperature eigen-exponent $y_t$.

Results are consistent with finite size scaling analysis.

Abstract

We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpi\'nski 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.