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 of the squareroot of 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 which is uniform in the configuration of the disorder, and so our proof shows that randomness will only enhance fluctuations.