Critical exponents of ferromagnetic Ising model on fractal lattices

Abstract

We review the value of the critical exponents $\nu^{-1}$, $\beta/\nu$, and $\gamma/\nu$ of ferromagnetic Ising model on fractal lattices of Hausdorff dimension between one and three. They are obtained by Monte Carlo simulation with the help of Wolff algorithm. The results are accurate enough to show that the hyperscaling law $d_f=2\beta/\nu+\gamma/\nu$ is satisfied in non-integer dimension. Nevertheless, the discrepancy between the simulation results and the $\epsilon$-expansion studies suggests that the strong universality should be adapted for the fractal lattices.