Scaling transition for nonlinear random fields with long-range dependence

We obtain a complete description of anisotropic scaling limits and the existence of scaling transition for nonlinear functions (Appell polynomials) of stationary linear random fields on $\mathbb{Z}^2$ with moving average coefficients decaying at possibly different rate in the horizontal and vertical direction. The paper extends recent results on scaling transition for linear random fields in Puplinskait\.e and Surgailis (2016), Puplinskait\.e and Surgailis (2015).