In Ginzburg-Landau theory the derivative terms in the free energy depend on the structure of the lattice1. That said when looking at e.g. the O(3)-model the only derivative term kept is $$(\vec \nabla \vec m)^2$$ however if the lattice is not completely isotropic other terms may exist e.g. $\partial_x \vec m \cdot \partial_y \vec m$. Is it possible to show that all such terms which are present for some lattice structures and not for others are irrelevant (in the renormalization group sense)?
1 This is mentioned in a number of sources e.g. (Giuseppe, 2013; pg224) and (Kardar, 2007; pg23)