Anisotropic variational principle for perturbed simply attractive potentials

Consider perturbed simply attractive potentials, including anisotropic potentials, meaning potentials that are not necessarily isotropic. Let the variational principle be the relation between specific free energy and surface tension for gradient Gibbs measures. Anisotropic variational-principle conjecture. The variational principle applies to all perturbed simply attractive potentials. The source says that the existing variational-principle results were proved only for isotropic potentials and for Lipschitz potentials in the discrete setting, so the anisotropic extension remains open.