  We study corrections to the scaling limit of subcritical long-range Ising
models with (super)-summable interactions on $\mathbb{Z}^d$. For a wide class
of models, the scaling limit is known to be white noise, as shown by Newman
(1980). In the specific case of couplings
$J_{x,y}=|x-y|^{-d-\boldsymbol{\alpha}}$, where $\boldsymbol{\alpha}>0$ and
$|\cdot|$ is the Euclidean norm, we find an emergence of fractional Gaussian
free field correlations in appropriately renormalised and rescaled observables.
The proof exploits the exact asymptotics of the two-point function, first
established by Newman and Spohn (1998), together with the rotational symmetry
of the interaction.
