Critical dynamics of the kinetic Ising model with triplet interaction on Sierpin-acuteski-gasket-type fractals.

Abstract

By use of the time-dependent renormalization-group method, the critical dynamics of the kinetic triplet-interaction Ising model on a family of Sierpin\ifmmode\acute\else\textasciiacute\fi{}ski-gasket-type fractals is studied. We find that for magneticlike perturbation the scaling law of the dynamic exponent has the form ${\mathit{z}}_{\mathit{M}}$=${\mathit{d}}_{\mathit{f}}$+3/\ensuremath{\nu}, where \ensuremath{\nu} is the static correlation exponent and independent of the member of the fractal family. However, for energylike perturbation, ${\mathit{z}}_{\mathit{E}}$=2/\ensuremath{\nu} and ${\mathit{z}}_{\mathit{E}}$ is independent of the member of the fractal family. In particular, for the two-dimensional Sierpin\ifmmode\acute\else\textasciiacute\fi{}ski gasket, ${\mathit{z}}_{\mathit{E}}$=${\mathit{z}}_{\mathit{M}}$=2/\ensuremath{\nu}=1/\ensuremath{\nu}+${\mathit{d}}_{\mathit{f}}$ is different from the result, z=1+${\mathit{d}}_{\mathit{f}}$, of the two-spin-interaction Ising model due to Achiam. This implies that the dynamic universality hypothesis is violated.