Dependence of scaling functions on spectral dimension

Determine whether the dependence of the voter-model ageing scaling functions solely on the spectral dimension, rather than separately on the geometric fractal dimension and spectral index, is a peculiarity of the voter model or a generic feature of systems on fractal substrates.

Background

The paper derives ageing scaling functions for the envelopes of the single-time and two-time correlators of the voter model on fractal substrates. Although the scaling variables depend on the spectral index θ, the resulting scaling functions depend only on the spectral dimension d_s. The authors explicitly ask whether this simplification is specific to the voter model or applies more broadly to nonequilibrium systems on fractal geometries. The question is left unresolved.