  In Puplinskaite and Surgailis (2014) we introduced the notion of scaling
transition for stationary random fields $X$ on $\mathbb{Z}^2$ in terms of
partial sums limits, or scaling limits, of $X$ over rectangles whose sides grow
at possibly different rate. The present paper establishes the existence of
scaling transition for a natural class of stationary Gaussian random fields on
$\mathbb{Z}^2$ with long-range dependence. The scaling limits of such random
fields are identified and characterized by dependence properties of rectangular
increments.
