Monte Carlo study of Ising spin dynamics on a fractal lattice

Abstract

The dynamics of Ising spins on a two-dimensional fractal lattice has been studied by Monte Carlo simulations. Both the limits $Lgg\ensuremath{\xi}$ and $Lll\ensuremath{\xi}$ were studied where $L$ is the size of the sample and $\ensuremath{\xi}$ the correlation length. Exact transfer matrix calculations were also carried out to check that the correct equilibrium values were reached. In both limits the predicted breakdown of conventional dynamic scaling was obtained. Using finite-size scaling $\ensuremath{\tau}\ensuremath{\sim}{L}^{z}$ for $Lll\ensuremath{\xi}$, an effective temperature-dependent critical exponent $z$ was obtained consistent with the recent prediction $z\ensuremath{\propto}\frac{1}{T}$ for small $T$.