Solution of crystal growth disorder models by imposition of symmetry

By considering the relation between Ising models and growth models, solutions have been obtained for a class of growth models in which symmetry has been imposed on the statistical properties of the lattices. It has been found that when mm symmetry is imposed the resulting two-point correlation field has an extremely simple form even though considerable diversity of three- and four-point correlations may still exist. It is suggested that imposition of symmetry on growth models in general will yield soluble systems.