  In this paper we complete the investigation of scaling limits of the odometer
in divisible sandpiles on $d$-dimensional tori generalising the works Chiarini
et al. (2018), Cipriani et al. (2017, 2018). Relaxing the assumption of
independence of the weights of the divisible sandpile, we generate generalised
Gaussian fields in the limit by specifying the Fourier multiplier of their
covariance kernel. In particular, using a Fourier multiplier approach, we can
recover fractional Gaussian fields of the form $(-\Delta)^{-(1+s)} W$ for $s>0$
and $W$ a spatial white noise on the $d$-dimensional unit torus.
