 Anisotropic effective dimension

The effective dimension for a specified anisotropic rescaling is the total scaling weight of its coordinate measure. With $D_{\perp }$ directions of weight 1 and $D_{\parallel }$ directions of weight $\theta$, $d_{\mathrm{eff}}=D_{\perp }+\theta D_{\parallel }$. The uniaxial Gaussian Lifshitz point has $\theta =1/2$, so $d_{\mathrm{eff}}=D-1/2$. This is not a topological or Hausdorff dimension.