A simple fluctuation lower bound for a disordered massless random continuous spin model in $d=2$

We prove a finite volume lower bound of the order \√log N on the delocalization of a disordered continuous spin model (resp. effective interface model) in $d=2$ in a box of size N. The interaction is assumed to be massless, possibly anharmonic and dominated from above by a Gaussian. Disorder is entering via a linear source term. For this model delocalization with the same rate is proved to take place already without disorder. We provide a bound that is uniform in the configuration of the disorder, and so our proof shows that disorder will only enhance fluctuations.